Tag: 统计

📚 Year 7 CAIE Statistics: Speaking & Listening Exam Preparation | 七年级CAIE统计：口语/听力备考专项

Welcome to your focused preparation guide for the speaking and listening components of Year 7 CAIE Statistics. This resource will help you build confidence in using statistical language aloud and understanding spoken descriptions of data, graphs, and calculations. Even though statistics is a mathematical subject, being able to discuss findings and interpret instructions verbally is a key skill assessed through oral and aural tasks.

欢迎使用这本针对七年级CAIE统计口语和听力部分的集中备考指南。本资料将帮助你建立大声使用统计语言以及理解口头描述数据、图表和计算的信心。虽然统计是一门数学学科，但能够口头讨论发现并解读指令是一项通过口语和听力任务来考核的关键技能。

1. Understanding Statistics Vocabulary | 理解统计学术语

Before you can speak or listen effectively in a statistics exam, you must be familiar with core terms. Key vocabulary includes data, survey, population, sample, frequency, variable, discrete, continuous, and categorical. Knowing these words by sight is not enough; you need to recognize them when spoken and pronounce them clearly yourself.

在统计考试中要有效地说或听，你必须熟悉核心术语。关键词汇包括数据、调查、总体、样本、频数、变量、离散型、连续型和分类型。仅仅看到认识这些词还不够；你需要能够在听到时识别它们，并能自己清晰地发音。

Common terms you will hear in instructions and questions:

你会在指令和问题中听到的常见术语：

• Mean, median, mode, range
• 平均数、中位数、众数、极差
• Bar chart, pictogram, line graph, pie chart
• 条形图、象形图、折线图、饼图
• Tally, frequency table, questionnaire
• 计数、频数表、问卷
• Axis, scale, interval, label
• 坐标轴、刻度、间距、标签

Make flashcards with the term on one side and a simple definition with an example on the other, and practise saying each word aloud.

制作一面是术语、另一面是简易定义附例子的抽认卡，并练习大声读出每个单词。

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2. Pronouncing Key Statistical Terms | 关键统计术语的发音

Correct pronunciation helps both you and your listener. Words like ‘continuous’ (con-tin-you-us) and ‘discrete’ (dis-creet) can be tricky. Break them into syllables and practise with a partner. Record yourself saying a list of terms and compare with a dictionary audio. Pay special attention to stress: in ‘frequency’, the stress is on the first syllable (FRE-quen-cy); in ‘questionnaire’, stress the last syllable (ques-tion-NAIRE).

正确发音有助于你本人和听者双方。像 ‘continuous’ (con-tin-you-us) 和 ‘discrete’ (dis-creet) 这样的词可能比较棘手。把它们拆分成音节并与伙伴一起练习。录下自己读术语列表的声音，并与词典音频作比较。特别留意重音：在 ‘frequency’ 中，重音在第一音节 (FRE-quen-cy)；在 ‘questionnaire’ 中，重音在最后一个音节 (ques-tion-NAIRE)。

Listen to how exam-style recordings say ‘x-axis’ and ‘y-axis’, and note that ‘mode’ rhymes with ‘road’, not ‘mod’. ‘Data’ can be pronounced DAY-ta or DAH-ta; both are acceptable, but try to be consistent. Practising with subject-specific audio clips will make you more comfortable during the listening test.

倾听考试风格的录音是如何说 ‘x-axis’ 和 ‘y-axis’ 的，并注意 ‘mode’ 与 ‘road’ 押韵，而不是 ‘mod’。’Data’ 可以读作 DAY-ta 或 DAH-ta；两种均可，但要力求一致。用学科专属的音频片段进行练习，会让你在听力测试时更加自如。

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3. Listening to Descriptions of Graphs and Charts | 听取图形和图表描述

A typical listening task might involve a teacher or recording describing a bar chart, and you need to sketch or answer questions. Key phrases to listen for include ‘the horizontal axis shows…’, ‘the vertical axis represents…’, ‘the bars are grouped by…’, ‘there is a sharp increase from… to…’. Train your ear to catch comparative language: ‘twice as many’, ‘half the number’, ‘greater than’, ‘fewer than’, ‘the same as’.

一个典型的听力任务可能包括一段教师或录音描述条形图，你需要画草图或回答问题。需要听取的关键短语包括 ‘the horizontal axis shows…’（横轴表示…）、’the vertical axis represents…’（纵轴代表…）、’the bars are grouped by…’（柱状图按…分组）、’there is a sharp increase from… to…’（从…到…急剧增长）。训练耳朵去捕捉比较性的语言：’twice as many’（两倍之多）、’half the number’（数量的一半）、’greater than’（大于）、’fewer than’（少于）、’the same as’（与…相同）。

When you practise, listen to short audio descriptions without looking at the graph first. Try to draw what you hear. Afterwards, check with the actual graph. Focus on the order of

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📚 Year 7 CAIE Statistics: Quick Vocabulary & Terminology Memorisation Guide | Year 7 CAIE 统计：词汇术语速记指南

Welcome to your Year 7 Statistics vocabulary guide. Mastering the key terms is the very first step towards understanding data, interpreting charts, and solving exam problems with confidence. This guide explains every essential word and phrase you are likely to meet in the CAIE course, with clear definitions and examples to help you remember them quickly.

欢迎使用七年级统计学术语指南。掌握关键术语是理解数据、解读图表并自信地解决考试问题的第一步。本指南解释了你将在 CAIE 课程中遇到的每一个重要词语和短语，配以清晰的定义和示例，帮助你快速记忆。

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1. What is Statistics? | 什么是统计？

Statistics is the branch of mathematics that deals with collecting, organising, interpreting, and presenting data. In your CAIE course, you will learn to work with numbers and categories to find patterns and answer questions. The word ‘data’ means pieces of information. The singular form is ‘datum’, but we nearly always say ‘data’ for a set of values.

统计学是数学的一个分支，研究数据的收集、整理、解释和呈现。在 CAIE 课程中，你将学习处理数字和类别，以发现模式并回答问题。“数据”一词指的是信息片段。单数形式是“datum”，但我们通常用“data”来表示一组数值。

A statistic is a fact or a number that summarises some data, such as an average or a percentage. Statistics helps us make sense of the world around us, from sports scores to weather forecasts.

统计量是概括某些数据的事实或数字，例如平均数或百分比。统计学帮助我们理解周围的世界，从体育比分到天气预报。

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2. Types of Data: Qualitative and Quantitative | 数据类型：定性数据与定量数据

Data can be split into two main types: qualitative and quantitative. Qualitative data (also called categorical data) describes qualities or categories. Examples include eye colour, favourite subject, and type of transport. Quantitative data is numerical and represents quantities that can be counted or measured. Examples are height in centimetres, number of siblings, and test scores.

数据可以分为两种主要类型：定性数据和定量数据。定性数据（也称为分类数据）描述性质或类别。例如眼睛颜色、最喜欢的科目和交通方式。定量数据是数值型数据，代表可计数或可测量的量。例如身高（厘米）、兄弟姐妹数量和考试分数。

When you collect data, always decide whether it is qualitative or quantitative. This choice affects which graph or average you will use later.

当你收集数据时，一定要判断它是定性的还是定量的。这个选择会影响你之后使用哪种图表或平均数。

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3. Discrete vs Continuous Data | 离散数据与连续数据

Quantitative data can be further divided into discrete and continuous data. Discrete data can only take certain values, usually whole numbers. You count discrete data. For example, the number of students in a class, goals scored in a match, or shoe size (even if it has halves, the values are fixed steps). Continuous data can take any value within a range and is measured rather than counted. Examples include time taken to run 100 m, weight, temperature, and length. Continuous data can include decimals and fractions.

定量数据可进一步分为离散数据和连续数据。离散数据只能取某些值，通常是整数。离散数据是数出来的。例如，班级学生人数、比赛进球数、鞋码（即使有半码，也是固定步长的值）。连续数据可以取一个范围内的任何数值，是测量出来的而不是数出来的。例如跑 100 米的时间、体重、温度、长度。连续数据可以包含小数和分数。

A simple memory trick: if you count it, it is probably discrete. If you measure it, it is continuous.

一个简单的记忆技巧：如果是数出来的，很可能是离散数据；如果是测量出来的，那就是连续数据。

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4. Population, Sample, and Census | 总体、样本与普查

When you study a group, the population is the whole group you want information about. For instance, all Year 7 students in your school. A sample is a smaller group chosen from the population. A census is when you collect data from every single member of the population. A sample is usually easier and quicker, but if it is not chosen carefully, it may not represent the whole population perfectly.

当你研究一个群体时，总体是你想要了解信息的整个群体。例如，你们学校所有七年级学生。样本是从总体中选出的较小群体。普查是指从总体的每一个成员那里收集数据。样本通常更容易、更快捷，但如果选择不慎，可能无法完美代表整个总体。

Key term: Bias. If a sample is not chosen fairly, it can lead to incorrect conclusions about the population.

关键术语：偏差。如果样本选择不公平，可能导致关于总体的错误结论。

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5. Frequency and Tally Charts | 频数与计数符号表

Frequency means how often something occurs. A frequency table shows categories or values along with their frequencies. To make counting easier, we use tally marks. A tally is a short stroke used to count items; every fifth stroke is drawn diagonally across the previous four to make a group of five. The tally column helps you count without missing any item.

频数表示某事发生的次数。频数表显示各个类别或数值及其频数。为了更方便计数，我们使用计数符号。计数符号是用来计数的短竖线；每五个为一组，第五条线斜着画过前四条竖线，形成一个“五条一组”的标记。计数符号栏帮助你计数而不遗漏任何项目。

• Red cars: |||| (4)
• Blue cars: |||| || (7)
• White cars: |||| |||| (10)

• 红色汽车：|||| (4)
• 蓝色汽车：|||| || (7)
• 白色汽车：|||| |||| (10)

Always use a key if your tally chart might be unclear. Counting systematically with tallies is an essential skill for data handling.

如果计数符号表可能不清晰，一定要使用图例。有系统地用计数符号计数是数据处理的基本技能。

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6. Averages: Mean, Median, and Mode | 平均数：均值、中位数和众数

An average is a value that represents the centre of a set of data. The three main averages are mean, median, and mode. The mean is found by adding all the values and then dividing by the number of values. The formula is shown below.

平均数是代表一组数据中心的值。三个主要的平均数是均值、中位数和众数。均值通过将所有数值相加再除以数值的个数得到。公式如下所示。

Mean = Σxᵢ ÷ n

The median is the middle value when the data is ordered from smallest to largest. If there are two middle numbers, find their mean. The mode is the value that appears most often. A data set can have one mode, more than one mode (called bimodal or multimodal), or no mode at all.

中位数是将数据从小到大排序后位于中间的值。如果有两个中间的数，就求它们的均值。众数是出现次数最多的值。一组数据可以有一个众数、多个众数（称为双众数或多众数），或者根本没有众数。

In exam questions, you will be asked to calculate these, so make sure you know the difference between them.

在考试题目中，会要求你计算这些值，因此务必清楚它们之间的区别。

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7. Range and Spread | 极差与离散程度

The range tells us how spread out the data is. It is the simplest measure of variation. The range is the difference between the largest and smallest values.

极差告诉我们数据的分散程度。它是最简单的离散程度度量。极差是最大值与最小值之间的差。

Range = Max − Min

A small range means the data values are close together; a large range means they are more spread out and varied. The range is not an average, but it is often used together with the mean or median to describe a data set.

极差小意味着数据值很接近；极差大意味着数据更加分散和多样化。极差不是平均数，但它常与均值或中位数一起用来描述一组数据。

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8. Graphs and Charts: Bar Charts, Pictograms, Pie Charts | 图表：条形图、象形图、饼图

To present data clearly, we use different types of chart. A bar chart uses rectangular bars of equal width. The height of each bar represents the frequency. Bar charts are excellent for comparing categories. A pictogram uses small pictures or symbols to represent data. Each picture stands for a certain number of items, and a key explains the scale. A pie chart (or circle graph) shows proportions of a whole. The entire circle represents the total, and each slice shows a category as part of that total. Pie charts are drawn by calculating angles.

为了清晰地展示数据，我们使用不同类型的图表。条形图使用等宽的长条，每个长条的高度代表频数。条形图非常适合比较各类别。象形图使用小图片或符号来代表数据。每个图片代表一定数量的物品，图例说明比例。饼图（或圆形图）显示整体中的比例。整个圆代表总数，每个扇形代表一个类别占总数的比例。饼图通过计算角度来绘制。

In Year 7, you need to be able to read and interpret these charts, and sometimes draw them yourself. Always label your axes, include a title, and pay attention to the scale.

在七年级，你需要能够阅读和解释这些图表，有时还需要自己绘制。始终标注坐标轴、添加标题，并注意比例尺。

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9. Probability: Likelihood Scale and Events | 概率：可能性量表和事件

Probability is the study of chance. It describes how likely an event is to happen. The probability of an impossible event is 0, and the probability of a certain event is 1. Probabilities can be written as fractions, decimals, or percentages. On the likelihood scale, we

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📚 Case Study: Statistical Analysis in Action | 案例分析实战演练：统计应用

In Year 7 Statistics, learning how to collect, organise, display and interpret data is essential. This case study walks you through a real classroom survey to show how statistical skills are applied in practice. Follow the steps to understand the full data handling cycle.

在七年级统计中，学习如何收集、整理、展示和解读数据至关重要。本案例将带你走进一个真实的课堂调查，展示如何将统计技能应用于实际。请跟随步骤，了解完整的数据处理流程。

1. Case Background | 案例背景

A Year 7 teacher wants to understand her students’ after-school habits. She decides to conduct a survey asking two questions: ‘What is your favourite sport?’ and ‘How many minutes do you spend on homework each day?’ The data collected will be used to teach statistical methods.

一位七年级老师想了解学生的课后习惯。她决定进行一项调查，提出两个问题：“你最喜欢的运动是什么？”和“你每天花多少分钟做作业？”收集到的数据将用于教授统计方法。

The survey is anonymous, and students are encouraged to give honest answers. The class has 32 students, all of whom participate.

此次调查为匿名形式，并鼓励学生如实作答。全班共有32名学生，均参加了调查。

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2. Research Questions: What Do We Want to Know? | 研究问题：我们想了解什么？

Before collecting data, it is crucial to define clear research questions. Our first question investigates students’ preferences for sports – this is categorical data. The second question examines the amount of time spent on homework – this is numerical data.

在收集数据之前，明确研究问题至关重要。第一个问题调查学生对运动的偏好——这是分类数据。第二个问题考察做作业所花的时间——这是数值数据。

Having both types of data allows us to practise a wide range of statistical techniques, from drawing charts to calculating averages and measures of spread.

拥有两种类型的数据使我们能够练习多种统计技巧，从绘制图表到计算平均数和离散度量。

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3. Data Collection Method | 数据收集方法

The teacher prepares a simple questionnaire. Each student writes down their favourite sport from a list (Football, Basketball, Swimming, Tennis, Other) and the number of minutes they spent on homework the previous day. Data is collected from all 32 students in the class.

老师准备了一份简单的问卷。每个学生从列表（足球、篮球、游泳、网球、其他）中写下自己最喜欢的运动，以及前一天用于做作业的分钟数。数据收集自全班32名学生。

To ensure accuracy, students are reminded to be honest and to record the homework time as accurately as possible. They are told to round their time to the nearest 5 minutes to simplify recording.

为确保准确性，提醒学生诚实作答并尽可能准确记录作业时间。他们被告知将时间四舍五入到最接近的5分钟，以简化记录。

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4. Dataset 1: Favourite Sports – Organising Categorical Data | 数据集1：最喜欢的运动——整理分类数据

Here are the raw results for favourite sports collected from 32 students: 12 chose Football, 8 Basketball, 6 Swimming, 4 Tennis and 2 selected Other. We can organise this into a frequency table.

以下是32名学生最喜欢的运动的原始结果：12人选择足球，8人篮球，6人游泳，4人网球，2人选其他。我们可以将其整理成频数表。

Sport (运动)	Frequency (频数)
Football (足球)	12
Basketball (篮球)	8
Swimming (游泳)	6
Tennis (网球)	4
Other (其他)	2
Total (总计)	32

This frequency table makes it easy to see the most and least popular sports. Football dominates with over a third of the votes, while ‘Other’ is the smallest group.

这张频数表便于我们观察最受欢迎和最不受欢迎的运动。足球以超过三分之一的票数占据主导地位，而“其他”是最小组。

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5. Visualising Categorical Data: Bar Charts and Pie Charts | 可视化分类数据：条形图和饼图

A bar chart is a great way to visualise categorical data. Each sport category is displayed on the horizontal axis, and the frequency on the vertical axis. For our data, the bar for Football would be the tallest at 12, followed by Basketball at 8, Swimming at 6, Tennis at 4, and Other at 2.

条形图是可视化分类数据的绝佳方式。每个运动类别显示在横轴上，频数显示在纵轴上。对于我们的数据，足球的条形最高为12，其次是篮球8，游泳6，网球4，其他2。

For a pie chart, we need to calculate the angle for each sector. Since there are 32 students in total, each student represents 360° ÷ 32 = 11.25°. We multiply each frequency by 11.25° to get the angle.

对于饼图，我们需要计算每个扇形的角度。因为总共有32名学生，每名学生代表360° ÷ 32 = 11.25°。将每个频数乘以11.25°即可得到角度。

Sport (运动)	Frequency (频数)	Angle (角度)
Football	12	135°
Basketball	8	90°
Swimming	6	67.5°
Tennis	4	45°
Other	2	22.5°

These angles are then used to draw the sectors using a protractor and compass. Always label each sector and include a title.

然后使用量角器和圆规根据这些角度画出扇形。务必给每个扇形贴上标签并加上标题。

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6. Dataset 2: Daily Homework Time – Numerical Data | 数据集2：每日作业时间——数值数据

The teacher also recorded the homework minutes for a subset of 15 students to study numerical data in more depth. The raw data, rounded to the nearest 5 minutes, is: 30, 45, 60, 30, 20, 45, 60, 90, 30, 45, 60, 40, 50, 30, 60.

老师还记录了其中15名学生的作业分钟数，以便更深入地研究数值数据。原始数据（四舍五入到5分钟）为：30, 45, 60, 30, 20, 45, 60, 90, 30, 45, 60, 40, 50, 30, 60。

These values are numerical and can be ordered from smallest to largest. Arranging them gives us: 20, 30, 30, 30, 30, 40, 45, 45, 45, 50, 60, 60, 60, 60, 90.

这些值是数值型，可以从小到大排序。排序后得到：20, 30, 30, 30, 30, 40, 45, 45, 45, 50, 60, 60, 60, 60, 90。

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7. Visualising Numerical Data: Dot

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📚 Year 7 CAIE Statistics: Mock Exam Paper Walkthrough | 7年级CAIE统计：单元测试模拟卷解析

This walkthrough is designed to help Year 7 students prepare for their CAIE Statistics unit test. We work through a full mock paper, question by question, covering data collection, charts, averages, spread, probability, and graph interpretation. Each section provides clear explanations, step-by-step solutions, and useful tips. By the end, you will feel confident tackling similar problems in your actual exam.

这套模拟卷解析专为7年级学生准备CAIE统计单元测试而设计。我们逐题讲解一份完整的模拟试卷，涵盖数据收集、图表、平均数、离散程度、概率以及图表解读。每节都提供了清晰的解释、分步解答和实用技巧。学完本文后，你将自信应对实际考试中的类似题目。

1. Data Collection, Tally Charts, and Frequency Tables | 数据收集、记数表与频数表

A survey asked 20 students to name their favourite fruit. The raw data collected is: Apple, Banana, Apple, Orange, Banana, Apple, Banana, Apple, Orange, Banana, Apple, Banana, Apple, Banana, Orange, Apple, Banana, Apple, Orange, Banana. To make sense of this list, we organise it using a tally chart and then a frequency table.

一项调查询问了20名学生他们最喜欢的水果。收集到的原始数据如下：苹果、香蕉、苹果、橙子、香蕉、苹果、香蕉、苹果、橙子、香蕉、苹果、香蕉、苹果、香蕉、橙子、苹果、香蕉、苹果、橙子、香蕉。为了理解这串数据，我们使用记数表进行整理，然后制作频数表。

Solution Steps:

解答步骤：

Step 1: Identify categories. The possible responses are Apple, Banana, and Orange. Write these as headings in the tally chart.

步骤1：确定类别。 可能的回答有苹果、香蕉和橙子。将这些作为记数表的标题。

Step 2: Tally each response. Go through the list one by one. For the first ‘Apple’, draw one vertical line in the tally column next to Apple. Continue this way, making a group of five tally marks (four vertical lines crossed with a diagonal slash) each time you reach five. After finishing, the tallies for Apple should show two full groups of five, Banana shows one group of five plus two, and Orange shows three individual marks.

步骤2：逐条记录。 逐一浏览列表。第一个“苹果”就在苹果旁边的记数列画一条竖线。如此继续，每满五条记数标记（四条竖线加一条斜线）就形成一组。完成后，苹果的记数应显示完整的两组五条，香蕉显示一组五条加两条，橙子显示三条单独的标记。

Step 3: Count frequencies. From the tally marks, count how many times each fruit appears. Apple: 10, Banana: 7, Orange: 3. Record these numbers in the frequency column. The total frequency is 10+7+3=20, which matches the number of students.

步骤3：数出频数。 根据记数标记，数出每种水果出现的次数。苹果：10，香蕉：7，橙子：3。将这些数字填入频数列。频数总和为10+7+3=20，与学生人数一致。

The completed frequency table looks like this:

完成的频数表如下：

Fruit	Tally	Frequency
Apple	卌 卌	10
Banana	卌 ||	7
Orange	|||	3
Total		20

Always check that the total frequency equals the number of data items originally collected.

务必检查频数总和是否等于最初收集的数据项数量。

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2. Bar Charts | 条形图

A bar chart is used to display the frequencies from the frequency table visually. Each category is represented by a rectangular bar whose height shows its frequency. The bars must be of equal width and equally spaced, and the chart needs a title and labeled axes.

条形图用于直观显示频数表中的频数。每个类别用一个矩形条表示，其高度代表频数。条形宽度必须相等、间距均匀，图表要有标题和带标签的轴。

Here is the mock question: ‘Draw a bar chart to represent the fruit frequency data.’ Let’s go through the construction.

下面是模拟题：“画一个条形图来表示水果频数数据。”我们来一步一步画。

Step 1: Draw and label the axes. The horizontal axis (x‑axis) shows the fruit categories: Apple, Banana, Orange. The vertical axis (y‑axis) shows the frequency. Choose a scale that goes up to at least the highest frequency (10). A scale of 1 square = 1 unit works well here.

步骤1：画出并标记轴。 横轴（x轴）表示水果类别：苹果、香蕉、橙子。纵轴（y轴）表示频数。选择一个刻度，最高至少要到最大频数（10）。此处用1格=1单位的刻度合适。

Step 2: Draw the bars. For Apple, draw a bar up to 10 on the y‑axis. For Banana, up to 7. For Orange, up to 3. All bars have the same width and do not touch each other.

步骤2：画出条形。 苹果对应画到纵轴10的高度；香蕉画到7；橙子画到3。所有条形宽度相同且彼此不接触。

Step 3: Add a title. Give the chart a clear title, such as ‘Favourite Fruit of 20 Students’.

步骤3：添加标题。 给图表起一个清晰的标题，例如“20名学生最喜欢的水果”。

The bar chart should clearly show that Apple is the most popular fruit, followed by Banana, then Orange.

条形图应清楚显示苹果最受欢迎，其次是香蕉，然后是橙子。

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3. Pictograms | 象形图

A pictogram uses symbols or pictures to represent data. Each symbol can stand for a certain number of items. In this mock question, we use a smiley face ☺ to represent 2 students. Construct a pictogram for the fruit data.

象形图用符号或图片来表示数据。每个符号可以代表一定数量的项目。在这道模拟题中，我们用一个笑脸☺代表2名学生。请为水果数据制作一个象形图。

Step 1: Determine the number of symbols for each category. Divide each frequency by 2 (since 1 ☺ = 2 students). Apple: 10 ÷ 2 = 5 smileys. Banana: 7 ÷ 2 = 3.5 → we need 3 full smileys and a half smiley to represent 1 student. Orange: 3 ÷ 2 = 1.5 → 1 full smiley and a half smiley.

步骤1：确定每个类别的符号数量。 将每个频数除以2（因为1个☺=2名学生）。苹果：10÷2=5个笑脸。香蕉：7÷2=3.5→需要3个完整笑脸和一个半笑脸代表1名学生。橙子：3÷2=1.5→1个完整笑脸和一个半笑脸。

Step 2: Draw the pictogram. Align the symbols in rows next to the fruit names. The half smiley is drawn as half of the smiley face. Remember to include a key: e.g., ‘☺ = 2 students’.

步骤2：绘制象形图。 将符号在水果名称旁边排成一行。半笑脸绘制成笑脸的一半。记得加上图例，例如“☺ = 2名学生”。

Step 3: Check totals. Apple: 5×2=10; Banana: 3×2+1=7; Orange: 1×2+1=3. This confirms the pictogram is correct.

步骤3：检查总数。 苹果：5×2=10；香蕉：3×2+1=7；橙子：1×2+1=3。这确认了象形图正确无误。

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4. Pie Charts | 饼图

A pie chart shows proportions by dividing a circle into sectors. The angle of each sector is calculated using the formula:

Angle = (Frequency ÷ Total frequency) × 360°

饼图通过将圆分成扇形来显示比例。每个扇形的角度用以下公式计算：

角度 = (频数 ÷ 总频数) × 360°

Using the fruit data: Total frequency = 20.

使用水果数据：总频数 = 20。

• Apple: (10 ÷ 20) × 360° = 0.5 × 360° = 180°
• Banana: (7 ÷ 20) × 360° = 0.35 × 360° = 126°
• Orange: (3 ÷ 20) × 360° = 0.15 × 360° = 54°

• 苹果：(10 ÷ 20) × 360° = 0.5 × 360° = 180°
• 香蕉：(7 ÷ 20) × 360° = 0.35 × 360° = 126°
• 橙子：(3 ÷ 20) × 360° = 0.15 × 360° = 54°

Check that the angles add up to 360°: 180°+126°+54° = 360°. Then draw the circle and use a protractor to mark the angles. Label each sector with the fruit name and percentage or frequency. The largest sector represents Apple, the most popular fruit.

检查角度总和是否为360°：180°+126°+54° = 360°。然后画圆，用量角器标出角度。每个扇区标上水果名称以及百分比或频数。最大的扇区代表苹果，最受欢迎的水果。

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5. Mean, Median, and Mode | 平均数、中位数与众数

This mock question presents the ages of seven children at a party: 12, 15, 13, 12, 18, 12, 10. Find the mean, median, and mode.

这道模拟题给出派对上七个孩子的年龄：12, 15, 13, 12, 18, 12, 10。请计算平均数、中位数和众数。

Mean: Add all values: 12+15+13+12+18+12+10 = 92. Divide by 7: 92 ÷ 7 ≈ 13.14 (to 2 decimal places).

Mean = 92 ÷ 7 ≈ 13.14

平均数： 将所有数值相加：12+15+13+12+18+12+10 = 92。除以7：92 ÷ 7 ≈ 13.14（保留两位小数）。

Median: First, order the numbers from smallest to largest: 10, 12, 12, 12, 13, 15, 18. The median is the middle value. Since there are 7 numbers, the 4th value is the median: 12.

中位数： 首先将数字从小到大排序：10, 12, 12, 12, 13, 15, 18。中位数是中间的值。因为有7个数字，第4个值就是中位数：12。

Mode: The mode is the number that appears most often. Here, 12 appears three times, while all others appear once. Thus, the mode is 12.

众数： 众数是出现次数最多的数字。这里12出现了三次，其他数字只出现一次。所以众数是12。

Remember: The mean gives the average, the median shows the middle, and the mode indicates the most frequent value.

记住：平均数给出平均值，中位数表示中间值，众数指出最常见的数值。

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6. Range | 极差

The range measures how spread out the data is. It is the difference between the largest and smallest values.

Range = Maximum – Minimum

极差衡量数据的分散程度。它是最大值与最小值之差。

极差 = 最大值 – 最小值

Using the same ages (10, 12, 12, 12, 13, 15, 18), the maximum is 18 and the minimum is 10. So the range = 18 – 10 = 8. A small range means the data values are close together; a large range shows they are more spread out.

使用同样的年龄数据（10, 12, 12, 12, 13, 15, 18），最大值为18，最小值为10。因此极差 = 18 – 10 = 8。极差小说明数据值比较集中；极差大表明它们分散得较开。

Always think about outliers. If an age of 45 were added, the range would become much larger, showing that one extreme value can greatly affect the range.

始终考虑异常值。如果加入一个45岁的年龄，极差会变得大得多，这表明一个极值能大幅影响极差。

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7. Introduction to Probability | 概率入门

Probability tells us how likely an event is to happen. We find it by dividing the number of favourable outcomes by the total number of possible outcomes.

Probability = Favourable outcomes ÷ Total outcomes

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📚 Year 7 CAIE Statistics: Practical Assessment Key Points | Year 7 CAIE 统计：实践考核要点

In Year 7 CAIE Statistics, the practical assessment is not just about getting the right answer — it’s about showing you can plan, collect, and analyse data in a scientific way. Examiners look for clear recording, sensible use of tools, and the ability to explain what your results mean. Mastering these skills early will also help you in science and everyday life.

在 Year 7 CAIE 统计中，实践考核不仅仅是得出正确答案，更是为了展示你能够科学地规划、收集和分析数据。考官注重清晰的记录、合理使用工具以及解释结果含义的能力。早日掌握这些技能也会在科学和日常生活中帮到你。

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1. Understanding the Goal of Your Investigation | 理解调查目标

Every practical task begins with a question or prediction. You might ask, “Do right-handed students have larger hand spans than left-handed students?” or “Does a warmer room make a candle burn faster?” Clarify the aim before collecting data.

每个实践任务都始于一个问题或预测。你可能会问：”右撇子学生的手掌跨度是否比左撇子学生大？”或者”温暖的房间是否会让蜡烛燃烧得更快？”在收集数据之前先明确目标。

A well-stated aim keeps your work focused. Avoid vague goals like “to see what happens” and instead use specific, measurable terms.

明确陈述的目标能让你的工作保持专注。避免使用”看看会发生什么”这类模糊的目标，而要用具体、可衡量的说法。

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2. Planning Data Collection and Sampling | 规划数据收集与抽样

Decide exactly what you will measure or observe, and how many times. If you can’t measure everyone, choose a sample that fairly represents the group. For instance, pick every fifth person on a register, not just your friends.

准确决定你将测量或观察什么，以及需要多少次。如果无法测量所有人，就选择一个能够公平代表整体的样本。比如，从花名册上每隔四人选一人，而不是只选你的朋友。

Create a simple data collection sheet in advance. Note what equipment you need, such as a ruler, timer, or questionnaire. Planning prevents rushed work during the assessment.

提前制作一张简单的数据收集表。记下你需要的器材，如尺子、计时器或问卷。提前规划可以避免考核时手忙脚乱。

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3. Identifying and Handling Variables | 识别和处理变量

In a comparative experiment, the factor you change on purpose is the independent variable (e.g., amount of water). The result you measure is the dependent variable (e.g., plant height). All other conditions must stay the same — these are control variables.

在比较型实验中，你有意改变的因素是自变量（如浇水量），你测量的结果是应变量（如植株高度）。其他所有条件都必须保持不变——这些是控制变量。

For a fair test, identify at least two control variables. For example, when comparing hand spans, control the type of ruler used and the way the hand is positioned. Fair testing makes your conclusions trustworthy.

为确保公平测试，至少要识别出两个控制变量。例如，在比较手掌跨度时，要控制所用的尺子类型和手的摆放方式。公平测试能让你的结论更加可信。

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4. Taking Accurate Measurements | 准确进行测量

Read the scale of your instrument carefully. Always read the ruler at eye level to avoid parallax error. If using a stopwatch, start timing at the exact moment the event begins and stop it promptly.

仔细阅读仪器上的刻度。读数时始终将尺子保持在视线水平以避免视差。如果使用秒表，要在事件开始时立即启动，并在结束时立即停止。

Record measurements to the correct precision. A ruler marked in millimetres should give readings like 12.3 cm, not just 12 cm. Estimate one place beyond the smallest division if possible, but do not invent extra digits.

以正确的精度记录测量值。刻度为毫米的尺子读数应像 12.3 厘米，而不只是 12 厘米。如果可能，估读到最小刻度下一位，但不要无中生有添加多余数字。

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5. Organising Data with Frequency Tables | 用频数表整理数据

For categorical data (e.g., favourite colours), use a tally chart. Each complete group of five tallies makes counting easier. Then write the frequency next to each category.

对于分类资料（如最喜欢的颜色），使用画记表。每五个画记为一组便于清点，然后在每个类别旁边写上频数。

For numerical data, you might group values into intervals, such as 0–4, 5–9, etc. Make sure intervals do not overlap. Record the frequency for each interval.

对于数值资料，你可以将数据分组到区间中，如 0–4，5–9 等。确保区间不重叠，并记录每个区间的频数。

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6. Creating Clear Statistical Charts | 绘制清晰的统计图表

A bar chart is suitable for categorical or discrete data. Draw bars of equal width, with gaps between them. Label both axes and give the chart a title, such as “Number of Students Choosing Each Sport”.

条形图适用于分类资料或离散资料。绘制宽度相等的条形，条形之间要留有空隙。给坐标轴加上标签，并为图表命名，例如”选择各项运动的学生人数”。

For continuous data or time series, use a line graph. Plot points accurately, then connect them with straight lines. Include a key if more than one set of data is plotted on the same graph.

对于连续资料或时间序列，使用折线图。精确描点后用直线连接。如果同一张图上有多组数据，要附加图例。

Pictograms use symbols to represent data. Choose a clear symbol and state what one symbol stands for. If a symbol represents 2 people, half a symbol can represent 1 person.

象形图用符号来表示数据。选择清晰易懂的符号，并标明每个符号代表什么。若一个符号代表 2 人，则半个符号就代表 1 人。

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7. Calculating Measures of Central Tendency and Spread | 计算集中趋势和离散程度的度量值

From a small set of data, you may be asked to find the mode (most frequent), median (middle value when ordered), and mean (total ÷ number of values). Show each step neatly.

你可能会被要求从一小批数据中找出众数（出现最频繁的值）、中位数（排序后居中的值）和平均数（总和 ÷ 数据个数）。请整洁地展示每一步骤。

For example, with values 5, 7, 8, 8, 10, the mode is 8, the median is 8, and the mean is (5+7+8+8+10) ÷ 5 = 7.6. Use brackets to show the sum before division.

例如，数据为 5、7、8、8、10，众数是 8，中位数是 8，平均数是 (5+7+8+8+10) ÷ 5 = 7.6。在除以数据个数之前，先用括号表示求和。

The range (maximum minus minimum) shows how spread out the data is. A large range might indicate inconsistency. Always write the range as a single number, e.g., Range = 10 – 5 = 5.

极差（最大值减最小值）显示数据的分散程度。极差大可能意味着数据不一致。注意将极差写成一个数字，如 极差 = 10 – 5 = 5。

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8. Interpreting Data and Graphs | 解读数据和图表

When looking at a chart, describe what you notice rather than just listing numbers. Use phrases like “more students chose football than any other sport” or “the line rises steeply between day 3 and day 5, showing faster growth”.

观察图表时，要描述你所注意到的情况，而不仅仅是罗列数字。可以使用这样的表述：”选择足球的学生比其他任何运动都多”，或者”折线在第三天到第五天之间急剧上升，显示生长加快”。

Compare categories or trends clearly. If you have a prediction, state whether the data supports it. A conclusion must be based on the evidence, not on what you expected to happen.

清晰地比较不同类别或趋势。如果你有一条预测，说明数据是否支持该预测。结论必须基于证据，而不是你期望发生的结果。

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9. Evaluating Your Investigation | 评估你的调查

After completing your practical work, reflect on its strengths and weaknesses. Were your measurements accurate? Did you have enough data points? Thinking critically about your method is a high-level skill.

完成实践工作后，反思其优点和不足。你的测量准确吗？你的数据点足够多吗？批判性地思考自己的方法是高阶技能。

Common issues include a sample that is too small, measurements taken at different times, or not controlling a variable properly. Suggest one or two realistic improvements for next time.

常见问题包括样本太小、测量时间不一致或未能恰当地控制变量。为下一次实验提出一

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📚 Year 7 CAIE Statistics: Top Scorers’ Tips for High Scores | Year 7 CAIE 统计：学霸高分经验分享

Statistics is not just about numbers – it’s about discovering patterns and making sense of information in everyday life. In Year 7 CAIE Statistics, you will learn how to collect data, draw graphs, and interpret what the data tells you. These top scorers’ tips will help you build a strong foundation, avoid common mistakes, and develop the confidence to tackle any statistics question with ease.

统计学不仅仅是关于数字——它关乎发现模式并理解日常生活中的信息。在 Year 7 CAIE 统计课程中，你将学习如何收集数据、绘制图表并解读数据所传达的信息。这些学霸的高分经验将帮助你打下坚实基础，避开常见错误，并培养信心，轻松应对任何统计问题。

1. Why Statistics Matters | 为什么统计学重要

Statistics helps us understand the world through data. From weather forecasts to sports scores, statistics allows us to make decisions based on evidence. In Year 7, you begin to see how data is collected, organized, and presented. Top students always connect what they learn to real-life situations – this makes the subject more interesting and easier to remember.

统计学帮助我们通过数据理解世界。从天气预报到体育比分，统计学让我们能够基于证据做出决策。在 Year 7，你开始了解数据如何被收集、整理和呈现。学霸们总是将所学内容与现实生活联系起来——这使学科更有趣，也更容易记忆。

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2. Mastering Key Concepts: Data Types and Collection | 掌握关键概念：数据类型与收集

You will come across two main types of data: categorical data (such as colours or favourite subjects) and numerical data (such as heights or test scores). A top scorer knows the difference clearly. Always check whether the data is discrete or continuous – discrete data can only take certain values (like number of siblings), while continuous data can take any value within a range (like height). For data collection, learn to design a simple survey with clear questions and use tally marks to record responses accurately.

你会遇到两种主要的数据类型：分类数据（如颜色或最喜欢的科目）和数值数据（如身高或测验分数）。学霸会清楚地区分它们。始终检查数据是离散的还是连续的——离散数据只能取某些特定值（如兄弟姐妹的数量），而连续数据在一个范围内可以取任何值（如身高）。关于数据收集，学会设计含有清晰问题的简单调查，并利用划记法准确记录回答。

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3. Organizing Data: Frequency Tables and Diagrams | 整理数据：频数表和图表

Organizing raw data into frequency tables is the first step of any statistical analysis. A high-scoring student always counts carefully and double-checks that the total frequency matches the number of data items. When constructing a frequency diagram, label both axes clearly and use a proper scale. For discrete data, leave gaps between bars; for continuous data, bars should touch. Small details like a ruler-drawn axis and a sharp pencil can earn you presentation marks.

将原始数据整理成频数表是任何统计分析的第一步。高分学生总是仔细计数，并再次检查总频数是否与数据项的数量一致。绘制频数图时，要清晰标注两轴并使用合适的刻度。对于离散数据，条形图之间要留有空隙；对于连续数据，条形应紧挨着。用尺子画坐标轴和削尖的铅笔这些细节都能为你赢得卷面分。

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4. Averages: Mean, Median, Mode, and Range | 平均数：均值、中位数、众数和极差

Year 7 introduces four key measures: mean, median, mode, and range. The mode is the most frequent value, the median is the middle value when data is ordered, the mean is the sum divided by the count, and the range measures spread (largest − smallest). Top scorers write down each step for mean calculations instead of doing it all mentally. When finding median, they always put the numbers in order first and check for an odd or even number of data points. Remember: a large range means the data is more spread out.

Year 7 介绍了四个关键指标：均值、中位数、众数和极差。众数是最频繁出现的值，中位数是将数据排序后中间的值，均值是总和除以个数，极差衡量数据的离散程度（最大值 − 最小值）。学霸在计算均值时会写出每一步，而不是全凭心算。在求中位数时，他们总是先把数字按顺序排好，并检查数据点的个数是奇数还是偶数。记住：极差大意味着数据更分散。

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5. Charts and Graphs: Bar Charts, Pictograms, Pie Charts | 图表：条形图、象形图、饼图

Each type of chart has a specific purpose. Bar charts compare categories easily; pictograms use symbols to show data – always include a key and keep symbols the same size. Pie charts show proportions of a whole. In CAIE exams, you may be asked to interpret or complete these charts. A top tip: when drawing a pie chart, remember that a full circle equals 360°, so each item’s angle = (its frequency ÷ total frequency) × 360°. Use a protractor carefully – a small error in angle can lead to marks being lost.

每种图表都有特定的用途。条形图便于比较类别；象形图用符号表示数据——一定要包含图例，并保持符号大小一致。饼图显示整体的各个部分所占的比例。在 CAIE 考试中，你可能会被要求解读或完成这些图表。一条重要技巧：画饼图时，记住整圆等于360°，因此每一项目的角度 =（其频数 ÷ 总频数）× 360°。仔细使用量角器——角度上的小误差可能会导致失分。

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6. Line Graphs and Scatter Plots | 折线图和散点图

Line graphs show changes over time and are drawn by connecting plotted points with straight lines. Always choose a scale that spreads the data across most of the graph paper – avoid squashing everything into one corner. Scatter plots show relationships between two sets of numerical data. Look for correlation: positive (upward slope), negative (downward slope), or no correlation. High achievers practice describing correlation in words as well as identifying patterns.

折线图显示随时间的变化，通过将描出的点用直线连接来绘制。始终选择一个能将数据分散在大部分坐标纸上的刻度——避免将所有数据挤在一个角落。散点图展示两组数值数据之间的关系。寻找相关性：正相关（向上倾斜）、负相关（向下倾斜）或无相关。高分学生不仅会识别模式，还会用文字描述相关性。

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7. Introduction to Probability: Basic Terms and Scale | 概率初步：基本术语和概率尺度

Probability tells us how likely an event is to happen. The probability scale runs from 0 (impossible) to 1 (certain). Learn these words: impossible, unlikely, even chance, likely, certain. You will often express probability as a fraction, for example, the probability of rolling a 3 on a fair die is 1/6. Top scorers always simplify fractions and check that the probability is between 0 and 1. If you get an answer like 3/2, you know something is wrong.

概率告诉我们一个事件发生的可能性大小。概率尺度从0（不可能）到1（必定发生）。记住这些词语：不可能、不太可能、机会均等、很可能、必定。你经常会将概率表示为分数，例如，投掷一枚公平骰子得到3的概率是 1/6。学霸总是化简分数，并检验概率是否在0和1之间。如果你得到像 3/2 这样的答案，你就知道出错了。

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8. Probability Experiments: Outcomes and Events | 概率实验：结果与事件

When you toss a coin or roll a dice, you carry out a probability experiment. The set of all possible outcomes is called the sample space. An event is one or more outcomes. For example, when rolling a dice, the event ‘even number’ includes outcomes 2, 4, 6. Top marks go to those who can list outcomes systematically without missing any. Use a grid or a table for combined events, such as tossing a coin and rolling a dice together.

当你抛硬币或掷骰子时，你就是在进行一个概率实验。所有可能结果的集合称为样本空间。事件指一个或多个结果。例如，掷骰子时，“偶数”这一事件包括2、4、6这些结果。能系统且不遗漏地列出结果的学生往往能拿到高分。对于组合事件，如同时抛硬币和掷骰子，可以使用网格或表格。

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9. Interpreting Statistical Diagrams: Common Mistakes | 解读统计图表：常见错误

Misreading scales and ignoring labels are two of the biggest pitfalls. Always read the title, the axis labels, and the units carefully. In a pictogram, check what one symbol represents; sometimes it’s more than 1. In bar charts, watch out for uneven class intervals – a wider bar might look taller but the frequency should be compared using area, not just height. Double-check your answers against the data given in the question – top students treat this as a habit.

误读刻度和忽略标签是两大常见陷阱。一定要仔细阅读标题、坐标轴标签和单位。在象形图中，检查每一个符号代表的数量；有时它代表不止1个单位。在条形图中，注意不均匀的组距——更宽的条形可能看起来更高，但频率的比较应基于面积而不只是高度。将你的答案与题目所给数据进行核对——学霸将此视为一个习惯。

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10. Exam Strategies: How to Score Full Marks | 考试策略：如何拿满分

In a CAIE Statistics exam, marks are awarded for method as well as the final answer. Show your working clearly – even if your final answer is wrong, you can still earn most of the marks. Read the question twice: the first time to understand, the second time to underline key numbers and command words like ‘calculate’, ‘draw’, or ‘compare’. Manage your time by allocating minutes based on marks; a 3-mark question should not take 15 minutes. At the end, if you have time, re-check calculations and ensure graphs are neat.

在 CAIE 统计学考试中，分数不仅给最终答案，还给解题方法。清晰地展示你的运算过程——即使最终答案错误，你仍能拿到大部分分数。题目读两遍：第一遍理解，第二遍划出关键数字和指令词，如“计算”、“画出”或“比较”。根据分数分配时间；一道3分的题不应花费15分钟。最后，如果还有时间，重新检查计算过程，并确保图表整洁。

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11. Revision Techniques: Making a Study Plan | 复习技巧：制定学习计划

Create a revision timetable that breaks topics into small chunks. Spend 25 minutes studying, then take a 5‑minute break – this is called the Pomodoro technique and keeps your brain fresh. Use flashcards for key formulas: mean = sum ÷ count, probability = favourable outcomes ÷ total outcomes, and angle for pie chart = (frequency ÷ total) × 360°. Practice past CAIE papers under timed conditions. Top scorers always make a note of mistakes and revise those topics the next day.

制定一个将各个主题分成小块的复习时间表。学习25分钟，然后休息5分钟——这被称为番茄工作法，能让大脑保持清醒。使用记忆卡片记关键公式：均值 = 总和 ÷ 个数，概率 = 有利结果数 ÷ 总结果数，饼图角度 =（频数 ÷ 总数）× 360°。在限时条件下练习 CAIE 历年真题。学霸总是将自己的错误记录下来，并在第二天复习这些主题。

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12. Final Thoughts: Stay Curious and Practice | 结语：保持好奇心，多加练习

Statistics becomes easier and more enjoyable when you are curious about the data around you. Look at charts in newspapers or on websites and ask yourself what they show. The more you practice, the faster and more accurate you become. Remember, every top scorer started exactly where you are now – with a willingness to learn and a commitment to regular practice. Believe in yourself, keep a positive attitude, and you will see your grades improve steadily.

当你对身边的数据感到好奇时，统计学就会变得更简单也更有趣。看看报纸或网站上的图表，问问自己它们展示了什么。你练习得越多，速度就越快，准确率也越高。记住，每一位学霸都曾站在和你们现在一样的起点上——带着学习的意愿和对定期练习的坚持。相信自己，保持积极态度，你会看到成绩稳步提升。

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📚 Year 7 CAIE Statistics: Comprehensive Syllabus Breakdown | Year 7 CAIE 统计：课程大纲全面解析

Welcome to your Year 7 Statistics journey. In this guide, we break down every part of the CAIE syllabus so you know exactly what to learn. Statistics is not just about numbers – it helps us understand the world through data, from sports scores to weather patterns. We will explore data types, graphs, averages, and even the basics of probability. Each section is explained clearly, with examples you can use straight away.

欢迎来到 Year 7 统计学习之旅。在这篇指南中，我们逐项拆解 CAIE 课程大纲，让你清楚掌握每一个知识点。统计不仅仅是关于数字，它能帮助我们通过数据理解世界，无论是体育比分还是天气变化。我们将探索数据类型、图表、平均数，甚至概率的基础。每个部分都用清晰的例子加以解释，方便你立刻上手。

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1. What is Statistics? | 什么是统计学？

Statistics is the science of collecting, organising, analysing, interpreting and presenting data. Data simply means information, often in the form of numbers or categories. In Year 7, you learn how to make sense of this information and draw meaningful conclusions from it.

统计学是收集、整理、分析、解读和呈现数据的科学。数据就是信息，通常以数字或类别形式出现。在 Year 7，你将学习如何理解这些信息并从中得出有意义的结论。

You will find that statistics is everywhere: in school reports, news articles, sports statistics and even in deciding which phone has the best battery life. The subject gives you a toolkit to ask questions and answer them using evidence.

你会发现统计无处不在：在学校成绩单里、新闻报道中、体育统计数据里，甚至在判断哪款手机电池续航最好时。这门学科给了你一套用证据提问和回答问题的工具箱。

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2. Types of Data | 数据类型

Data is divided into two main types: qualitative and quantitative. Qualitative data describes qualities or categories, like favourite colour or type of pet. It is also called categorical data.

数据分为两大类型：定性数据和定量数据。定性数据描述性质或类别，比如最喜欢的颜色或宠物的种类，它也被称为分类数据。

Quantitative data deals with numbers and amounts. This type is further split into discrete and continuous. Discrete data can only take certain values, often counted (e.g. number of students in a class). Continuous data can take any value within a range and is measured (e.g. height, temperature).

定量数据涉及数字和数量。这种类型可以进一步分为离散数据和连续数据。离散数据只能取某些特定的值，通常是计数得到的（例如班级学生人数）。连续数据可以在一个范围内取任意值，是通过测量得到的（例如身高、温度）。

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3. Collecting Data | 数据收集

Before you can analyse anything, you need to gather data. Common methods include surveys, questionnaires, observations and experiments. In Year 7, you will often design a simple survey to collect information from your classmates.

在分析任何数据之前，你需要先收集数据。常见的方法包括调查、问卷、观察和实验。在 Year 7，你经常会设计一个简单的调查来从同学那里收集信息。

It is crucial to ask clear, unbiased questions. For example, asking ‘Do you agree that football is the best sport?’ may lead responses, while ‘Which sport do you prefer: football, basketball or tennis?’ gives fairer data.

提出清晰、不带偏见的问题至关重要。例如，问“你同意足球是最好的运动吗？”可能会引导答案，而问“你更喜欢哪项运动：足球、篮球还是网球？”则能得到更公平的数据。

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4. Organising Data with Frequency Tables | 用频数表组织数据

Once data is collected, it must be organised. A frequency table shows how often each item or category occurs. It is one of the simplest and most powerful tools in statistics.

数据收集后必须进行整理。频数表显示了每个项目或类别出现的次数，是统计中最简单也最强大的工具之一。

Tally marks are used to record raw data quickly. Each group of five is marked as four vertical lines crossed by a fifth line. After counting tallies, you fill in the frequency column. This helps you see patterns at a glance.

计数记号用于快速记录原始数据。每五个为一组，用四条竖线和一条横穿斜线表示。清点完计数值后，再填写频数列。这能让你一眼看出数据的分布模式。

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5. Bar Charts and Pictograms | 条形图与象形图

A bar chart represents categorical data using rectangular bars. The length or height of each bar corresponds to its frequency. Bars should be of equal width and spaced evenly.

条形图用矩形条表示分类数据，每个条形的长度或高度与其频数对应。条形应当宽度相等且均匀间隔。

A pictogram uses small pictures or symbols to show data. Each picture represents a certain number of items, shown in a key. Both bar charts and pictograms must have a clear title and labelled axes.

象形图使用小图片或符号来表示数据。每个图片代表一定数量的项目，这通常在图例中说明。条形图和象形图都必须具备清晰的标题和标注过的坐标轴。

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6. Pie Charts | 饼图

A pie chart is a circle divided into slices, where each slice shows the proportion of a category relative to the whole. They are excellent for comparing parts to a total.

饼图是一个被划分成扇形的圆形图，每个扇形显示某个类别相对于整体的比例。饼图特别适合将各部分与总数进行比较。

To draw a pie chart, you must find the angle for each category using the formula:

Angle = (Category Frequency ÷ Total Frequency) × 360°

要画饼图，你需要用下面的公式计算每个类别的角度：

角度 = (类别频数 ÷ 总频数) × 360°

Always check that all your angles add up to 360°. Use a protractor to measure the angles accurately on your circle.

一定要检查所有角度加起来等于 360°。用半圆规在圆上精确量出角度。

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7. Line Graphs | 线状图

Line graphs are used to display data that changes over time. Points are plotted for each time interval and connected with straight lines, showing trends and patterns.

线状图用于显示随时间变化的数据。在每个时间间隔上标出数据点，并用直线连接起来，以展现趋势和模式。

Time always goes on the horizontal (x) axis, and the measured quantity on the vertical (y) axis. For example, you could plot temperature readings taken every hour to see how the weather warms up during the day.

时间总是放在横轴（x 轴），而测量的量放在纵轴（y 轴）。例如，你可以绘制每小时记录的气温读数，看看白天天气如何变暖。

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8. Averages: Mean, Median and Mode | 平均数：均值、中位数和众数

An average is a single value that summarises the centre of a data set. In Year 7 you learn three types: mean, median and mode.

平均数是概括数据中心趋势的单一数值。在 Year 7，你将学习三种平均数：均值、中位数和众数。

The mode is the value that appears most often. A set can have one mode, more than one mode, or no mode at all. It is the easiest average to spot.

众数是出现最频繁的数值。一组数据可以有一个众数、多个众数，或者没有众数。它是最容易识别的平均数。

The median is the middle value when the data is listed in order. If there is an even number of values, the median is the mean of the two middle numbers. The order step is essential.

中位数是将数据按顺序排列后位于中间的那个值。如果数据个数为偶数，中位数就是中间两个数的均值。排序这个步骤必不可少。

The mean is calculated by adding all values together and dividing by how many values there are:

Mean = Sum of all values ÷ Number of values

均值是将所有数值相加再除以数据个数得到的：

均值 = 所有数值之和 ÷ 数据个数

For the set {4, 5, 8, 3}, the sum is 20 and there are 4 numbers, so the mean is 5. The mean can be influenced by extreme values.

对于数据集 {4, 5, 8, 3}，总和为 20，有 4 个数，因此均值为 5。均值可能会受到极端数值的影响。

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9. Range and Spread | 极差与数据分布

While averages tell us about the centre, the range tells us how spread out the data is. It is the simplest measure of spread.

平均数告诉我们数据的中心在哪，而极差告诉我们数据的分散程度。它是最简单的离散程度衡量指标。

Range = Largest value – Smallest value

极差 = 最大值 – 最小值

A small range means the data points are close together; a large range means they are more spread out. For example, the range of {2, 3, 4, 8} is 8 – 2 = 6.

极差小意味着数据点比较集中；极差大则表示数据较为分散。例如，{2, 3, 4, 8} 的极差是 8 – 2 = 6。

Comparing ranges helps you understand consistency. Test scores with a small range show the whole class performed similarly, while a large range suggests varied performance.

比较极差有助于理解数据的一致性。极差小的测试成绩表明全班表现接近，而极差大则说明成绩差异较大。

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10. Introduction to Probability | 概率入门

Probability is the branch of mathematics that deals with chance. It measures how likely an event is to happen.

概率是数学中处理机会大小的分支。它衡量一个事件发生的可能性有多大。

The probability scale goes from 0 (impossible) to 1 (certain). An event with a probability of ½ (0.5) has an even chance, like getting heads when you flip a fair coin.

概率的范围从 0（不可能）到 1（必然）。概率为 ½（0.5）的事件意味着机会均等，比如抛一枚公平硬币得到正面朝上。

The basic probability formula is:

Probability = Number of favourable outcomes ÷ Total number of possible outcomes

基本概率公式为：

概率 = 有利结果的数量 ÷ 所有可能结果的总数

If you roll a fair six‑sided die, the probability of rolling a 3 is 1 ÷ 6, which simplifies to 1/6.

如果掷一个公平的六面骰子，掷出 3 点的概率是 1 ÷ 6，化简为 1/6。

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11. Comparing and Interpreting Data | 数据的比较与解读

Real statistical work involves comparing two or more sets of data. You might compare the favourite subjects of boys and girls or the temperature trends of two different weeks.

真正的统计工作涉及比较两组或多组数据。你可能会比较男生和女生最喜欢的科目，或者两周不同的气温变化趋势。

When comparing, always look at both averages and spread. For instance, if the mean marks of two classes are similar, check the range: a lower range suggests more consistent performance.

在比较时，既要看平均数也要看数据的分布。例如，如果两个班级的平均成绩相近，就检查极差：极差较小意味着表现更稳定。

Also pay attention to what the charts and tables are really telling you. Ask questions like: Is the sample size large enough? Is the data fairly collected? These critical thinking skills are part of being statistically literate.

还要留意图表和表格真正传递的信息。提问如下：样本量够大吗？数据是公平收集的吗？这些批判性思维技能是具备统计素养的一部分。

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📚 Year 7 CAIE Statistics: Core Concepts Summary | 核心知识点梳理

Welcome to your comprehensive revision guide for Year 7 CAIE Statistics. This article brings together every key concept you need to master, from collecting and organising data to interpreting graphs, calculating averages and understanding basic probability.

欢迎阅读 Year 7 CAIE 统计学综合复习指南。本文整理了所有你需要掌握的核心概念，涵盖数据收集与整理、图表解读、平均数计算及概率基础。

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1. Types of Data | 数据类型

In Year 7 statistics, data is classified as either categorical or numerical. Categorical data describes qualities or groups, such as favourite colour or pet type. Numerical data represents quantities and can be discrete (countable, like the number of siblings) or continuous (measured, like height or time).

在七年级统计中，数据分为分类数据和数值数据。分类数据描述品质或组别，如最喜欢的颜色或宠物种类。数值数据表示数量，可以是离散型（可数，如兄弟姐妹个数）或连续型（测量得出，如身高或时间）。

Understanding the data type helps you choose the best graph and the appropriate average.

了解数据类型有助于你选择最合适的图表及恰当的平均数。

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2. Collecting Data | 数据收集

Data can be collected through surveys, questionnaires, or observations. A common method is to use a tally chart, where each data value is recorded with tally marks. A group of five is shown by four vertical strokes and one diagonal crossing stroke.

数据可通过调查、问卷或观察来收集。常用方法是使用计数符号表，每个数据值用计数字号记录。五个一组表示为四条竖线加一条斜线。

Clear data collection helps you avoid mistakes before you even start making tables or graphs.

清晰的数据收集能让你在绘制表格或图表之前就避免错误。

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3. Frequency Tables | 频数表

A frequency table organises data by listing each value alongside how many times it occurs (its frequency). Tally marks are often converted into numerical frequencies to make the table neat and ready for graphing.

频数表将数据按数值列出，并对应其出现的次数（频数）。计数符号通常转换为数字频数，使表格整洁且便于绘制图表。

Always check that the sum of the frequencies equals the total number of data points.

务必检查频数总和等于数据点的总数。

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4. Bar Charts | 条形图

Bar charts display categorical or discrete data using rectangular bars. The height (or length) of each bar represents the frequency. Bars are drawn with equal widths and equal gaps between them. Always label both axes and give the chart a title.

条形图用矩形条展示分类或离散数据。每个条的高度（或长度）代表频数。条形等宽，条间等距。必须标注两轴并给出图表标题。

Bar charts make it easy to compare how common different categories are at a glance.

条形图让不同类别的常见程度一目了然。

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5. Pictograms | 象形图

A pictogram uses pictures or symbols to represent data. A key tells you how many units one symbol stands for. For example, one smiley face might represent two people. Half symbols are used when the number is not a whole multiple of the key value.

象形图用图片或符号表示数据。图例说明一个符号代表多少个单位。例如，一个笑脸可能代表两个人。当数据不是图例值的整数倍时，使用半个符号。

Pictograms are visually attractive but must be drawn carefully so the key is accurate.

象形图视觉吸引力强，但绘制时必须确保图例准确无误。

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6. Line Graphs | 折线图

Line graphs are used to show changes over time or continuous sequences. Points are plotted and connected by straight line segments. The horizontal axis usually shows time or order, and the vertical axis shows the measured quantity.

折线图用于展示随时间或连续序列的变化。先描点，再用直线段连接。横轴通常表示时间或顺序，纵轴表示测量的数量。

Look for trends, such as increasing, decreasing or staying constant.

观察趋势，如上升、下降或保持不变。

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7. Pie Charts | 饼图

A pie chart shows how a whole is divided into parts. Each sector represents a category, and its angle is proportional to the frequency. The formula for the angle is:

饼图展示一个整体如何被分成若干部分。每个扇区代表一个类别，其角度与频数成正比。计算角度的公式为：

Angle = (Category frequency ÷ Total frequency) × 360°

角度 = (类别频数 ÷ 总频数) × 360°

Always use a protractor to draw the angles and label each sector or add a key.

始终用量角器绘制角度，并标注每个扇区或添加图例。

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8. Mean, Median and Mode | 平均数、中位数和众数

Averages help summarise a data set with a single typical value. The three main averages are the mean, median and mode.

平均数用一个典型值概括一组数据。三种主要平均数是平均数、中位数和众数。

The mean is calculated by adding all values and dividing by the number of values.

平均数的计算方法是把所有数值相加再除以数值个数。

Mean = Sum of all values ÷ Number of values

平均数 = 所有数值之和 ÷ 数值总数

The median is the middle value when the data is arranged in order. If there are two middle numbers, the median is their average.

中位数是将数据排序后中间的那个值。如果有两个中间数，中位数是这两个数的平均数。

The mode is the value that appears most often. A data set can have one mode, more than one mode, or no mode at all.

众数是出现次数最多的数值。一个数据集可以有一个众数、多个众数或没有众数。

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9. Range | 极差

The range measures how spread out the data is. It is the difference between the largest and the smallest values.

极差衡量数据的分散程度，它是最大值与最小值之差。

Range = Largest value − Smallest value

极差 = 最大值 − 最小值

A small range means the data points are close together; a large range means they are more spread out.

极差小表示数据点比较集中；极差大表示数据分布更分散。

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10. Comparing Data Sets | 数据组比较

To compare two sets of data, you can use an average (mean, median or mode) and the range. The average tells you which set is generally higher or lower, while the range tells you which set is more varied.

要比较两组数据，你可以使用一个平均数（平均数、中位数或众数）和极差。平均数告诉你哪一组整体上偏高或偏低，而极差告诉你哪一组变化更大。

For example, if Class A has a higher mean score but a smaller range than Class B, Class A performed better on average and more consistently.

例如，如果A班的平均分数较高但极差较小，那么A班平均表现更好且更稳定。

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11. Basic Probability | 概率基础

Probability describes how likely an event is to happen. It can be written as a fraction, decimal or percentage on a scale from 0 (impossible) to 1 (certain).

概率描述一个事件发生的可能性。它可以用分数、小数或百分数表示，尺度从0（不可能）到1（确定）。

For equally likely outcomes, the probability of an event is:

对于等可能结果，事件的概率为：

Probability = Number of favourable outcomes ÷ Total number of possible outcomes

概率 = 有利结果数 ÷ 所有可能结果总数

Probability helps you predict what might happen in experiments like rolling a fair dice or flipping a coin.

概率帮助你预测在抛硬币或掷骰子等实验中可能发生的结果。

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📚 Year 7 CAIE Statistics: Vocabulary and Terminology Quick Memory Guide | Year 7 CAIE 统计：词汇术语速记指南

Mastering the language of statistics is just like learning the rules of a new game – once you know the key words, everything starts to make sense. This quick memory guide introduces the most important vocabulary you will meet in Year 7 CAIE Statistics. For each term we give a simple definition, a memorable trick and a practical example so you can recall it instantly in class, in homework or during a test.

掌握统计学的语言就像学习一种新游戏的规则——一旦熟悉了关键词，一切都变得清晰起来。这份速记指南为你介绍 Year 7 CAIE 统计中最核心的词汇。每个术语都配有简单的定义、好记的窍门和实用的例子，让你在课堂、作业或考试中立刻就能回想起来。

1. Data and Information | 数据与信息

Data is a collection of raw facts, numbers, symbols or measurements that have not yet been organised. Think of data as the individual puzzle pieces – they exist but they don’t tell a story on their own. Information is data that has been sorted, analysed or presented in a way that makes it meaningful. Memory hook: ‘Data’ sounds like ‘dated facts’ – facts that have been recorded, while ‘Information’ has the word ‘inform’ inside it, because it informs you of something.

数据是一堆尚未整理过的原始事实、数字、符号或测量值。可以把数据想象成一块块的拼图碎片——它们存在但本身讲述不出完整的故事。信息则是经过排序、分析或以有意义的方式呈现出来的数据。记忆窍门：‘Data’听起来像‘达特’，可以联想成‘达到特写的记录’，而‘Information’里有‘inform’，因为信息会告知你一些事情。

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2. Population and Sample | 总体与样本

In statistics, a population is the entire set of people, objects or events you want to study. A sample is a smaller group selected from the population, used to draw conclusions about the whole population without checking every single member. Memory trick: ‘Population’ contains ‘pop’ – think of a popular music star with many fans, that’s everyone. ‘Sample’ sounds like ‘small example’ – a tiny taste of the whole group.

在统计学中，总体是你想研究的全部人员、物品或事件。样本是从总体中选出的较小群体，用来推断总体的情况而无需调查每一个成员。记忆技巧：‘Population’里有‘pop’，让人想到流行歌手拥有大量粉丝，那就是所有人；‘Sample’听起来像‘small example’——一小份样品，代表整个总体。

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3. Types of Data: Categorical and Numerical | 数据类型：分类数据与数值数据

Categorical data describes qualities or groups that cannot be measured with numbers in the usual sense, such as hair colour, favourite fruit or pet type. Numerical data is made up of numbers you can calculate with, like height, test scores or the number of siblings. Numerical data can be further split into discrete data, which can only take certain values (e.g. number of cars in a driveway – you cannot have 2.5 cars), and continuous data, which can take any value within a range (e.g. a person’s height can be 154.6 cm). Memory aid: ‘Categorical’ starts with ‘cat’ – imagine sorting cats into different coloured baskets. ‘Numerical’ has ‘number’ hidden inside it, so you know it involves digits.

分类数据描述的是不能用普通数字来度量的性质或组别，比如发色、喜爱的水果或宠物种类。数值数据则是由可以计算的数字组成，比如身高、考试成绩或兄弟姐妹的个数。数值数据还可以细分为离散数据，只能取特定的值（例如车道上停放的汽车数量，不可能有2.5辆），以及连续数据，可以在一个范围内取任意值（例如一个人的身高可以是154.6厘米）。记忆窍门：‘Categorical’开头是‘cat’，想象把不同颜色的猫放进对应的篮子；‘Numerical’里藏着‘number’，说明它和数字有关。

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4. Tally Marks and Frequency | 计数符号与频率

A tally is a quick way of counting using short lines, with every fifth line drawn diagonally through the first four to make a group of five. Frequency is the number of times a particular data value occurs, often recorded in a frequency table next to tally marks. Memory hook: ‘Tally’ rhymes with ‘valley’ – picture a shepherd counting sheep with lines on a stick as they cross a valley. ‘Frequency’ sounds like ‘frequent see’ – how frequently you see a certain item in your list.

计数符号是一种用短线快速计数的方法，每数到第五个就用一条斜线穿过前四条，形成一组五。频率是指某个数据值出现的次数，通常和计数符号一起记录在频率表里。记忆窍门：‘Tally’读起来像‘塔利’，想象牧羊人数羊，每数一只就在木棍上刻一道。‘Frequency’听起来像‘frequent see’——你经常看见某个项目出现的频繁程度。

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5. Mean – The Average | 平均数

The mean is found by adding up all the values in a data set and then dividing the total by the number of values. It gives the central value that balances the data. The mean is often called the average, although in statistics there are other types of average too. Memory image: The word ‘mean’ sounds like ‘bean’. Imagine you have a pot of beans and you want to share them equally among your friends – you count all the beans, then divide by the number of friends. That’s exactly what the mean does.

把一组数据里所有的数值加起来，再用总和除以数值的个数，就得到平均数。平均数提供了一个使数据平衡的中心值。虽然我们常说‘平均值’，统计中还有其他类型的平均数。记忆画面：‘Mean’的发音像‘蜜’，想象你有一罐蜜豆，想平均分给朋友们——你先数出总豆数，再除以朋友人数，这就是平均数的做法。

Mean = (Sum of all values) ÷ (Number of values)

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6. Median – The Middle Value | 中位数

The median is the middle number in a sorted list of values. To find it, arrange the numbers from smallest to largest and pick the one in the centre. If there are two middle numbers, the median is their average. Memory trick: ‘Median’ sounds like ‘medium’ – the medium size is right in the middle of small and large. You can also think of the median strip in the middle of a road that separates two lanes; the median value separates the higher half from the lower half of a data set.

中位数是一组排序后的数值里最中间的那个数。先从小到大排列数据，再找到正中的那个。如果有两个中间数，中位数就是它们的平均数。记忆技巧：‘Median’的发音像‘medium’——中号正好位于小号和大号之间。你还可以联想马路中间的分隔带 median strip，它把道路分成两半；中位数也正好把数据分成较高的一半和较低的一半。

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7. Mode – The Most Frequent | 众数

The mode is the value that appears most often in a data set. A set of data can have one mode, more than one mode (bimodal or multimodal) or no mode at all if no number repeats. Mode is especially useful for categorical data, e.g. the most popular colour chosen in a survey. Memory image: ‘Mode’ sounds like ‘mood’ or ‘model’ – think of the fashion model wearing the most popular style of the season. The mode is simply what is ‘in fashion’ most frequently in your data.

众数是一组数据中出现次数最多的值。一组数据可以有一个众数、多个众数（双众数或多众数），如果所有数都只出现一次则没有众数。众数在处理分类数据时特别有用，比如调查中最受欢迎的颜色。记忆画面：‘Mode’的发音像‘模’，让人想到T台上模特展示的最流行款式。众数就是数据里最‘时髦’、出现最频繁的那个值。

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8. Range – The Spread | 极差

The range measures how spread out a set of data is. It is calculated by subtracting the smallest value from the largest value. A small range means the data are closely packed together, while a large range shows they are widely scattered. Memory hook: A mountain range contains the lowest valley and the highest peak – the range is the difference between these extremes. Whenever you hear ‘range’, picture a rangy landscape and subtract the bottom from the top.

极差衡量一组数据的分散程度，计算方法是最大值减去最小值。极差小说明数据集中紧密，极差大则表明数据分布很广。记忆窍门：山脉 range 包含最低的山谷和最高的山峰——极差正是这两个极端之间的差距。每当听到‘range’，就想象一片起伏的山野，用最高点减去最低点。

Range = Highest value − Lowest value

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9. Bar Charts and Pictograms | 条形图与象形图

A bar chart uses rectangular bars of equal width to represent data, with the length of each bar showing the frequency or value for each category. The bars can be drawn vertically or horizontally and there are gaps between them to show the categories are separate. A pictogram uses simple pictures or symbols to represent data, where each picture stands for a certain number of items. Memory aid: ‘Bar’ reminds you of a bar of chocolate – rectangles lined up to compare. ‘Pictogram’ contains ‘picture’, so it is a diagram made of pictures.

条形图用宽度相等的长方形条块来表示数据，每个条块的长度代表相应类别的频率或数值。条块可以竖着画也可以横着画，条与条之间留有空隙，显示类别是分开的。象形图用简单的图画或符号表示数据，每个图画代表一定数量的项目。记忆方法：‘Bar’让人想到一块块巧克力，排在一起方便比较；‘Pictogram’里藏着‘picture’，所以是用图画构成的统计图。

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10. Pie Charts and Sector Angles | 饼图与扇形角度

A pie chart is a circular chart divided into sectors, where each sector represents a proportion of the whole. The angle of each sector, called the sector angle, is calculated using the formula below. The whole circle represents 360°. Pie charts are ideal for showing how a total is split into parts. Memory helper: Think of a real pie cut into slices – the bigger the slice, the larger the angle and the larger the share. ‘Sector’ sounds like ‘section’ of a circle.

饼图是一个被分成若干扇形的圆形统计图，每个扇形代表整体的一部分。每个扇形的角度叫做扇形角度，可以通过下面的公式计算。整个圆代表360°。饼图特别适合展示一个总体如何分割成各个部分。记忆帮手：把饼图想象成一张被切开的大饼——扇形越大角度越大，所占份额也就越大。‘Sector’听起来像‘section（部分）’，就是圆的一部分。

Sector angle = (Frequency of category ÷ Total frequency) × 360°

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11. Surveys and Questionnaires | 调查与问卷

A survey is a method of collecting data by asking people questions. The set of questions given to people is called a questionnaire. Good questions should be clear, unbiased and easy to answer. Closed questions have a limited set of answers (e.g. Yes/No), while open questions allow people to write freely. Memory image: ‘Survey’ sounds like ‘to view over’ – you are looking over people’s opinions. ‘Questionnaire’ has ‘question’ inside it, suggesting a paper full of questions.

调查是通过提问来收集数据的一种方法，发给人们的那套问题就叫做问卷。好的问题应当清楚、不带偏见而且容易回答。封闭式问题只有有限的几种答案（例如是/否），开放式问题则允许人们自由作答。记忆画面：‘Survey’就像‘俯瞰’——你在概括地查看大家的看法；‘Questionnaire’里面直接有‘question’，暗示它是一张写满问题的纸。

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12. Probability Words: Certain, Likely, Unlikely and More | 概率词汇：确定、可能、不太可能等

Probability describes how likely an event is to happen. We use words placed on a scale from impossible to certain. ‘Impossible’ means 0 chance, ‘

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📚 Year 7 CAIE Statistics: Essay Writing Framework and Sample Essay | Year 7 CAIE 统计：论文写作框架与范文

In Year 7 CAIE Statistics, you are often asked to write a short essay or report to explain your findings from data. This might feel challenging at first, but once you learn a clear writing framework, you will be able to structure your ideas logically and score high marks. This guide will walk you through every step of building a strong statistical essay, from understanding the task to polishing your conclusion. We will also study a full sample essay on screen time data, so you can see exactly how to apply these skills.

在 Year 7 CAIE 统计课程中，你经常需要写一篇短文或报告来解释从数据中得到的发现。一开始这可能感觉很有挑战性，但一旦你学会了一个清晰的写作框架，你就能逻辑清晰地组织想法并获得高分。本指南将带你走过构建一篇优秀统计论文的每一步，从理解任务到润色结论。我们还会研读一篇关于屏幕时间数据的完整范文，让你直观地看到如何运用这些技能。

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1. Understanding the Task | 理解任务

Before you begin writing, read the question carefully. A typical Year 7 statistics essay question provides a data set, a graph or a table, and asks you to describe, compare and interpret the information. Look for command words such as ‘describe’, ‘compare’, ‘calculate’ and ‘explain’. These words tell you exactly what you must include. Remember that you are not simply repeating numbers; you are telling a story about what the data shows and why it matters.

在开始写作之前，仔细阅读题目。一道典型的 Year 7 统计论文题会提供一个数据集、一张图表或一张表格，并要求你描述、比较和解读信息。请注意指令词，例如 ‘describe’、’compare’、’calculate’ 和 ‘explain’。这些词精确地告诉你必须包含什么。请记住，你不是在简单地重复数字；你是在讲述数据所展示的故事以及它为什么重要。

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2. Planning Your Response | 规划你的回答

Spend five minutes making a quick plan. Jot down the key sections: introduction, data description, calculations, interpretation and conclusion. Under each heading, list the main points in bullet form. For example, under ‘data description’ you might write ‘Highest value 30 hours, lowest 8 hours’. This plan will keep your essay organised and prevent you from forgetting important steps. A well-planned answer always scores better than one written in a rush.

花五分钟做一个快速的计划。写下关键部分：引言、数据描述、计算、解读和结论。在每个标题下，以要点形式列出主要内容。例如，在“数据描述”下你可能会写“最高值30小时，最低值8小时”。这个计划会让你的文章有条理，并防止你遗忘重要步骤。有充分计划的答案总是比匆忙写成的答案得分更高。

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3. Introduction: Setting the Scene | 引言：设定背景

Your introduction should be two or three sentences long. State what the data is about, where it came from and what your report will do. For instance: ‘This report analyses the weekly screen time (in hours) of 20 Year 7 students. The data was collected through a class survey. It will describe the distribution, calculate the average and discuss what the results suggest about students’ habits.’ Keep it concise and to the point.

你的引言应该有两三句话。说明数据是关于什么的、来自哪里以及你的报告将会做什么。例如：“本报告分析了20名 Year 7 学生每周的屏幕时间（以小时计）。数据通过班级调查收集。报告将描述分布情况，计算平均值，并讨论结果对学生习惯的提示。”保持简洁、切中要点。

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4. Describing Data: Words and Numbers | 描述数据：文字与数字

Begin your description by stating the range and any extreme values. Use comparative language such as ‘more than’, ‘less than’, ‘the highest’ and ‘the lowest’. For example: ‘The screen time ranged from 8 hours to 30 hours per week, a difference of 22 hours. Six students spent more than 18 hours, which is noticeably above the rest.’ Always link numbers to real meaning, and do not just list figures without explanation.

通过陈述范围和任何极端值来开始你的描述。使用比较性语言，例如“多于”、“少于”、“最高的”和“最低的”。例如：“屏幕时间从每周8小时到30小时不等，差距达22小时。有六名学生花费超过18小时，明显高于其余学生。”始终将数字与实际意义联系起来，不要只列出数字而不加解释。

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5. Calculating Central Tendency and Spread | 计算集中趋势与离散程度

For Year 7, you must calculate the mean, median, mode and range if the data allows. Show your working clearly. The formulas are:

对于 Year 7，如果数据允许，你必须计算平均数、中位数、众数和极差。清楚地展示你的计算过程。公式如下：

Mean = Sum of all values ÷ Number of values

平均数 = 所有数值之和 ÷ 数值个数

Always interpret what these measures tell you. For instance, if the mean is higher than the median, the data may be skewed by a few very large numbers. Mention which average is the most representative and why.

始终要解读这些度量告诉了你什么。例如，如果平均数高于中位数，数据可能因几个非常大的数值而产生偏斜。提及哪个平均数最具代表性以及为什么。

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6. Interpreting Your Findings | 解读你的发现

Interpretation is where you explain what the statistics mean in real life. Do not simply say ‘the mean is 15.2 hours’. Instead, write: ‘The mean of 15.2 hours suggests that, on average, students spend just over two hours per day on screens. This is close to the recommended daily limit, but the wide range shows that some students far exceed it.’ Linking numbers to context demonstrates higher-order thinking.

解读是你解释统计结果在现实生活中意味着什么的地方。不要只说“平均数是15.2小时”。而要这样写：“15.2小时的平均数表明，学生平均每天花费略多于两小时在屏幕上。这与每日推荐时长接近，但很宽的极差表明一些学生远远超出了这一时长。”将数字与情境联系起来展示了你更高层次的思维。

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7. Comparing Groups or Categories | 比较组别或类别

If your data contains two groups, such as boys and girls, or different year groups, you must compare them using averages and spread. Use phrases like ‘On average, boys spent 3 hours more per week than girls’ or ‘The girls’ data was less spread out, with a range of only 10 hours compared to 18 hours for the boys.’ Always support comparisons with calculated figures.

如果你的数据包含两组，例如男生和女生，或者不同年级，你必须使用平均数和离散程度进行比较。使用诸如“平均而言，男生每周比女生多花3小时”或“女生的数据分布更集中，极差仅为10小时，而男生为18小时”等短语。始终用计算出的数字来支持比较。

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8. Structuring a Conclusion | 构建结论

Your conclusion should summarise the main findings without introducing new numbers. Restate the typical value or pattern and reflect on what the data suggests. A strong conclusion might also give a simple recommendation, such as ‘It would be useful to survey more students across different schools to see if this pattern is widespread.’ Keep the conclusion brief but thoughtful.

你的结论应该总结主要发现，而不引入新的数字。重申典型值或模式，并反思数据所提示的内容。一个有力的结论也可以给出简单的建议，例如“调查更多来自不同学校的学生，以观察这种模式是否普遍，将会很有用”。结论要简短，但要有思想性。

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9. Worked Example: Analysing Screen Time Data | 范文实例：分析屏幕时间数据

The following example uses a data set of weekly screen time (in hours) for 20 Year 7 students: 8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 18, 20, 22, 25, 30. Read how the framework is applied in a full essay response.

以下示例使用了一组20名 Year 7 学生每周屏幕时间（小时）的数据：8, 9, 10, 10, 11, 12, 12, 13, 13, 14, 14, 15, 15, 16, 17, 18, 20, 22, 25, 30。阅读如何将框架应用到一篇完整的论文回答中。

Introduction
This report analyses the weekly screen time of 20 Year 7 students from a class survey. It will describe the spread of the data, calculate key averages and discuss what the findings might mean for students’ screen habits.

引言
本报告分析了一项班级调查中20名 Year 7 学生每周的屏幕时间。它将描述数据的分布情况，计算关键的平均数，并讨论这些发现对学生屏幕习惯可能意味着什么。

Data Description
Screen time ranged from 8 hours to 30 hours, giving a range of 22 hours. The lowest value, 8 hours, belonged to only one student, while the highest, 30 hours, was an outlier far above the rest. The majority of students fell between 10 and 18 hours. The distribution appeared slightly skewed to the upper end, as a few individuals recorded notably high screen usage.

数据描述
屏幕时间从8小时到30小时不等，极差为22小时。最低值8小时仅来自一名学生，而最高值30小时是一个远超其余人的异常值。大多数学生落在10到18小时之间。分布似乎向高端略有偏斜，因为少数人记录到了明显较高的屏幕使用时间。

Calculations
The sum of all values is 304. Therefore, the mean is 304 ÷ 20 = 15.2 hours. To find the median, I ordered the data: the 10th and 11th values are both 14, so the median is 14 hours. The mode is not clearly defined because several values (12, 13, 14, 15) appear twice. The range, as noted, is 30 – 8 = 22 hours.

计算
所有数值之和为304。因此，平均数为304 ÷ 20 = 15.2小时。为求中位数，我将数据排序：第10和第11个值都是14，因此中位数为14小时。众数并不明确，因为多个数值（12、13、14、15）都出现了两次。如前所述，极差为30 – 8 = 22小时。

Interpretation
The mean (15.2 hours) is higher than the median (14 hours), which tells us that a few very high screen times are pulling the average upwards. The median of 14 hours, or 2 hours per day, is probably a better representation of a typical student. However, the large range of 22 hours highlights significant inequality: some students have very little screen time, while one student spends more than 4 hours per day. This could indicate different access to devices or different family rules.

解读
平均数（15.2小时）高于中位数（14小时），这告诉我们少数非常高的屏幕时间拉高了平均值。中位数14小时，即每天2小时，可能更好地代表了一个典型学生。然而，22小时的大极差突显了显著的不平等：一些学生屏幕时间很少，而一名学生每天超过4小时。这可能表明对电子设备的不同接触机会或不同的家庭规则。

Conclusion
In summary, the typical Year 7 student in this class spends around 14 hours per week on screens, but there are large individual differences. The data suggests that while many follow moderate habits, a few may be at risk of excessive use. A larger survey including different classes and questions about the type of screen activity would give a fuller picture.

结论
总之，该班级中典型的 Year 7 学生每周花费约14小时在屏幕上，但个体差异很大。数据表明，虽然许多人遵循适度习惯，但少数人可能有过度使用的风险。一项包括不同班级以及关于屏幕活动类型问题的大规模调查将提供更全面的图景。

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10. Marking Criteria and Top Tips | 评分标准与高分技巧

Examiners look for four main features: accurate calculations, clear description, sensible interpretation and good structure. You gain extra credit when you explain why you chose a particular average, discuss the shape of the data, and link numbers to real-world meaning. Always check your arithmetic and reread your essay to correct any spelling or grammar mistakes.

考官看重四个主要特征：准确的计算、清晰的描述、合理的解读和良好的结构。当你解释为什么选择某个特定的平均数、讨论数据的形态以及将数字与现实意义联系起来时，你会获得额外的加分。务必检查你的计算，并重读你的文章以纠正任何拼写或语法错误。

Top tips:

高分技巧：

• Use the words ‘mean’, ‘median’, ‘mode’ and ‘range’ accurately. Never call the range an ‘average’.
• 正确使用 ‘mean’、’median’、’mode’ 和 ‘range’ 这些词。绝不要把极差称为“平均数”。
• Include units (hours, cm, kg) every time you state a number.
• 每次陈述数字时都要包含单位（小时、厘米、千克）。
• Connect your paragraphs with linking words: ‘furthermore’, ‘in contrast’, ‘overall’.
• 用连接词连接你的段落：’furthermore’、’in contrast’、’overall’。
• Show all steps in your calculations, even if the question does not ask you to.
• 展示计算过程中的所有步骤，即使题目没有要求你这样做。

Practice writing one full essay per topic from your scheme of work. With each attempt, you will become faster and more confident.

从你的教学大纲中，每个主题练习写一篇完整的文章。随着每次尝试，你会变得更快、更自信。

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📚 Common Misconceptions and Correction Methods in Year 7 CAIE Statistics | 7年级CAIE统计常见误区与纠正方法

Statistics at Year 7 level introduces fundamental ideas like averages, charts and probability. Many students at this stage develop stubborn misunderstandings that can affect later learning. This article highlights ten common misconceptions and shows clear correction methods, helping learners build a solid foundation for CAIE assessments.

七年级统计学引入了平均数、图表和概率等基本概念。许多学生在这个阶段会形成顽固的误解，影响后续学习。本文列举了十个常见误区，并给出了清晰的纠正方法，帮助学习者打下应对CAIE评估的坚实基础。

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1. Mean, Median and Mode Are the Same | 误区：平均数、中位数和众数是相同的

Students often think ‘average’ means one single number and that the mean, median and mode are just different names for that same value. They might calculate only the mean and claim they have found the median.

学生常认为“平均值”只是一个单一数值，而平均数、中位数和众数只是同一个值的不同叫法。他们可能只计算了平均数，就宣称找到了中位数。

In truth, each measure of central tendency describes data differently. The mean is the sum divided by the count, the median is the middle ordered value, and the mode is the most frequent value. In the data set {1, 2, 2, 9, 100}, the mean is 22.8, the median is 2, and the mode is 2 — they can be far apart.

事实上，每种集中趋势度量描述数据的方式都不同。平均数是用总和除以个数，中位数是排序后中间的值，众数是出现次数最多的值。在数据集 {1, 2, 2, 9, 100} 中，平均数是 22.8，中位数是 2，众数是 2 —— 它们可能相差很远。

Correction method: Always define each term before selecting a value. Use a comparison table to reinforce differences.

纠正方法： 在选取数值前，先定义每个术语。可使用对比表来强化区别。

Measure	How to find it
Mean	Sum of all data ÷ number of values
Median	Middle value after ordering (average of two middle if even count)
Mode	Value that appears most often

Mean = (Sum of all values) ÷ Number of values

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2. The Range Is a Type of Average | 误区：极差是一种平均数

Because the range is taught alongside mean, median and mode, some learners automatically treat it as another average. They might say ‘the average spread’ or even call the range ‘the average of the data’.

由于极差是和平均数、中位数、众数一起讲授的，一些学生自然把它也当成一种平均数。他们可能会说“平均离散程度”，甚至称极差为“数据的平均数”。

The range is a measure of spread, not central tendency. It simply tells us how far apart the smallest and largest values are. In {3, 5, 8, 12}, the range is 9, but none of these numbers is an average.

极差是离散程度的度量，不是集中趋势。它只是告诉我们最小值和最大值相差多远。在 {3, 5, 8, 12} 中，极差是 9，但其中没有一个是平均数。

Correction method: Introduce the range with the phrase ‘spread’ rather than ‘average’. Show that range = maximum – minimum, and contrast it directly with the mean.

Range = Maximum value – Minimum value

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3. The Mode Is the Frequency, Not the Data Value | 误区：众数是频数，而不是数据值本身

A common slip occurs when students look at a frequency table and pick the highest frequency number as the mode. For example, if ‘blue’ appears 7 times and ‘red’ appears 4 times, they may write ‘7’ as the mode instead of ‘blue’.

一个常见的失误是，学生在看频数表时，把最高的频数当作众数。例如，如果“蓝色”出现了 7 次，“红色”出现了 4 次，他们可能会把“7”写成众数，而不是“蓝色”。

The mode is the category or value with the highest frequency, not the frequency itself. In the example, the mode is ‘blue’ because it occurs most often.

众数是具有最高频数的类别或数值，而不是频数本身。在上例中，众数是“蓝色”，因为它出现的次数最多。

Correction method: Emphasise the question ‘Which item appears most?’ rather than ‘Which number is biggest?’ Use colour-coded examples to separate frequency from label.

纠正方法： 强调“哪一个项目出现最多？”而不是“哪一个数字最大？”用颜色编码的例子把频数与标签区分开。

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4. The Median Is Just the Middle Number in an Unsorted List | 误区：中位数就是未排序列表中间的那个数

Given a list like 8, 3, 5, 9, 1, a student might point to the third number (5) and call it the median, without rearranging the data.

给定一个列表，如 8, 3, 5, 9, 1，学生可能会直接指向第三个数（5）并称其为中位数，而没有重新排列数据。

The median can only be found after ordering the values from smallest to largest. The ordered list is 1, 3, 5, 8, 9, so the median is 5 — in this case it coincidentally matches, but if the list were 8, 3, 9, 1, 5, the unsorted middle is still 9, which would be wrong.

中位数只有在将数值从小到大排序后，才能找到。有序列表是 1, 3, 5, 8, 9，中位数是 5——在这里是巧合匹配，但如果列表是 8, 3, 9, 1, 5，未排序的中间数仍是 9，那就错了。

Correction method: Instill a routine: ‘Order first, then find position.’ For an even number of values, teach that the median is the mean of the two middle numbers.

纠正方法： 培养习惯：“先排序，再找位置”。对于偶数个数值，教导中位数是中间两个数的平均数。

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5. Pie Chart Slices Must Be Equal in Size | 误区：饼图中的扇区大小必须相等

Many beginners assume that because a pie chart looks like a divided circle, each slice should take the same angle. They struggle to accept that a slice representing 50% of the data should be a semicircle.

许多初学者认为，因为饼图看起来像一个被分割的圆，所以每个扇区角度应该相同。他们很难接受代表 50% 数据的扇区应该是一个半圆。

In a pie chart, the size of each sector is proportional to the frequency or percentage it represents. A category with 30% of the data gets an angle of 0.30 × 360° = 108°, not 90°.

在饼图中，每个扇区的大小与其代表的频数或百分比成比例。一个占 30% 数据的类别，其角度是 0.30 × 360° = 108°，而不是 90°。

Correction method: Relate pie charts to fractions of a whole. Practise calculating sector angles: angle = (frequency ÷ total frequency) × 360°. Let students draw sectors with protractors to see the variation.

Sector angle = (Frequency for category ÷ Total frequency) × 360°

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6. Bar Charts Can Have Bars Touching Like a Histogram | 误区：条形图可以像直方图一样条形紧挨着

Students sometimes see bars in a bar chart and think they should touch, especially if they have encountered a ‘block graph’ earlier. They may draw bar charts with no gaps between bars.

学生有时看到条形图中的条形，就认为它们应该紧挨着，特别是如果之前见过“块状图”。他们可能画出的条形图条形之间没有间隙。

A bar chart represents categorical (discrete) data, so there should be equal gaps between bars to show the categories are separate. Only histograms (used for continuous data) have bars that touch, and that concept is usually introduced later.

条形图表示分类（离散）数据，因此条形之间应有相等的空隙，以显示类别是分开的。只有直方图（用于连续数据）的条形是紧挨的，而直方图的概念通常晚些介绍。

Correction method: Label bar charts as ‘categorical’ and always draw a gap. Show side-by-side examples of bar charts (gaps) and simple picture graphs to highlight the difference.

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7. Probability Can Be Greater Than 1 or Less Than 0 | 误区：概率可以大于 1 或小于 0

When asked to write the probability of an event, some pupils produce numbers like 1.5 or –0.2, thinking probability works like any other number line. They might say “150% sure”.

当被要求写出某个事件的概率时，一些学生会给出 1.5 或 –0.2 之类的数字，以为概率就像普通的数轴一样。他们可能会说“150% 肯定”。

Probability is always between 0 and 1 inclusive. A probability of 0 means impossible, 1 means certain. Probabilities can be expressed as fractions, decimals or percentages (0% to 100%), but never outside these limits.

概率总是在 0 到 1 之间（含 0 和 1）。概率为 0 表示不可能，1 表示必然。概率可以用分数、小数或百分数（0% 到 100%）表示，但绝不能超出这些界限。

Correction method: Use a probability scale line from 0 to 1, placing words ‘impossible’, ‘unlikely’, ‘even chance’, ‘likely’, ‘certain’. When calculating, remind students that the number of successful outcomes cannot exceed the total number of outcomes.

0 ≤ Probability ≤ 1

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8. If Something Hasn’t Happened for a While, It Is ‘Due’ to Happen | 误区：某件事很久没发生，就“该”发生了

In games with dice or coins, a learner may observe several tails in a row and say, ‘Heads is due next,’ believing the coin somehow balances itself.

在掷骰子或抛硬币的游戏中，学生观察到连续几次反面后可能会说：“正面该出现了”，认为硬币会设法平衡自己。

If a coin is fair, each toss is independent. The probability of heads remains ½ every time, regardless of previous outcomes. This faulty belief is known as the gambler’s fallacy.

如果硬币是均匀的，每次抛掷都是独立的。无论之前结果如何，出现正面的概率每次都是 ½。这种错误观念被称为赌徒谬误。

Correction method: Conduct experiments with many tosses and record runs. Show that long sequences of the same side occur naturally without any ‘due’ mechanism. Emphasise independence of events.

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9. A Larger Sample Always Gives Better Data | 误区：样本越大数据一定越好

Students often believe that if they ask more people, their results will automatically be more accurate. They overlook bias in how the sample is chosen.

学生通常认为只要询问更多的人，结果就会自动变得更准确。他们忽视了样本选择方式带来的偏差。

A large but biased sample (e.g., surveying only Year 7 boys about school lunch preferences) will still give misleading conclusions. Quality of sampling — randomness and representation — matters more than size alone.

一个大却带有偏差的样本（例如，只调查七年级男生对学校午餐的偏好）仍然会导致误导性结论。样本的质量——随机性和代表性——比单纯的大小更重要。

Correction method: Role-play biased versus random sampling. Show how a small random sample can be more accurate than a large biased one. Use the phrase ‘fair sample’ to stress the idea.

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10. The Mean Must Be One of the Data Values | 误区：平均数一定是数据值之一

When the result of the mean calculation is a decimal that does not appear in the original set, some students feel it is wrong and round it or change it to fit an existing number.

当平均数计算结果是小数，而这个小数在原数据集中并未出现时，一些学生会觉得算错了，于是四舍五入，或者把这个数改成已有的某个数。

The mean is a calculated balance point and does not need to be an actual data value. In family size data {2, 3, 4}, the mean is 3, which does appear, but in {1, 2, 3, 4} the mean is 2.5, which is not a family size — and that is perfectly acceptable.

平均数是一个计算出的平衡点，不需要是实际的数据值。在家庭人数数据 {2, 3, 4} 中，平均数是 3，恰好出现；但在 {1, 2, 3, 4} 中平均数是 2.5，不是一个可能的家庭人数——而这完全合理。

Correction method: Use a number‑line model with counters to show the mean as a physical balance point. Repeatedly state that the mean can be a fraction or decimal, even when data are whole numbers.

Mean = (1 + 2 + 3 + 4) ÷ 4 = 10 ÷ 4 = 2.5

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Published by TutorHao | Statistics Revision Series | aleveler.com

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📚 Year 7 CAIE Statistics: Unit Test Mock Paper Walkthrough | Year 7 CAIE 统计：单元测试模拟卷解析

This article provides a complete walkthrough of a Year 7 CAIE Statistics mock unit test. Each question is presented with a clear solution and key learning points. Work through all ten questions to revise data collection, representation, averages, and range — all aligned with the Cambridge Lower Secondary curriculum.

本文提供一套 Year 7 CAIE 统计单元模拟测试题的完整解析。每道题目均配有清晰的解题过程和关键知识点讲解。请逐一完成这十道题目，以复习数据收集、数据展示、平均数和极差等内容——所有题目均贴合剑桥初中课程要求。

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1. Finding the Mode | 找出众数

The shoe sizes of ten students are recorded: 4, 5, 5, 6, 4, 5, 7, 6, 5, 8. Identify the mode of this data set.

十名学生的鞋码记录如下：4, 5, 5, 6, 4, 5, 7, 6, 5, 8。请找出这组数据的众数。

To find the mode, count how many times each number appears. The number 4 appears twice, 5 appears four times, 6 appears twice, 7 appears once, and 8 appears once. The mode is the value that occurs most often, which is 5.

找众数时，需要数出每个数值出现的次数。数字 4 出现了两次，5 出现了四次，6 出现了两次，7 出现了一次，8 出现了一次。众数是出现次数最多的数值，因此众数为 5。

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2. Finding the Median | 找出中位数

The test scores of seven pupils are: 11, 14, 9, 18, 13, 10, 16. Work out the median score.

七名学生的测验分数为：11, 14, 9, 18, 13, 10, 16。请计算中位数分数。

First, write the numbers in ascending order: 9, 10, 11, 13, 14, 16, 18. With seven values, the median is the middle number, which is the 4th value — 13. So the median score is 13.

首先将数字按升序排列：9, 10, 11, 13, 14, 16, 18。一共有七个数值，中位数是位于正中间的数，即第 4 个数——13。因此中位数分数为 13。

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3. Calculating the Mean | 计算平均数

A survey asks eight friends how many pets they own. The responses are: 2, 0, 1, 3, 2, 4, 1, 3. Calculate the mean number of pets.

一项调查询问了八位朋友各自养了多少只宠物，回答如下：2, 0, 1, 3, 2, 4, 1, 3。请计算平均宠物数量。

Add all the values together: 2 + 0 + 1 + 3 + 2 + 4 + 1 + 3 = 16. There are 8 responses. Divide the total by the number of values: 16 ÷ 8 = 2. The mean number of pets is 2.

将所有数值相加：2 + 0 + 1 + 3 + 2 + 4 + 1 + 3 = 16。一共有 8 个回答。用总和除以数值的个数：16 ÷ 8 = 2。平均宠物数量为 2 只。

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4. Finding the Range | 找出极差

The maximum daily temperatures (in °C) for one week are: 12, 15, 11, 18, 14, 13, 17. What is the range of these temperatures?

一周内每日最高气温（单位：°C）为：12, 15, 11, 18, 14, 13, 17。这些气温的极差是多少？

The range is the difference between the largest and smallest values. The highest temperature is 18 °C and the lowest is 11 °C. Subtract: 18 – 11 = 7. The range is 7 °C.

极差是最大值与最小值之间的差值。最高气温为 18 °C，最低气温为 11 °C。相减得：18 – 11 = 7。极差为 7 °C。

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5. Tally Charts and Frequency Tables | 划记表与频数表

Twenty students were asked their favourite colour. The raw data is: Red, Blue, Blue, Green, Red, Red, Yellow, Blue, Green, Red, Blue, Yellow, Red, Green, Blue, Red, Blue, Green, Red, Blue. Complete a frequency table and state which colour is the mode.

向二十名学生询问了他们最喜欢的颜色，原始数据为：红、蓝、蓝、绿、红、红、黄、蓝、绿、红、蓝、黄、红、绿、蓝、红、蓝、绿、红、蓝。请完成频数表，并说出众数是哪种颜色。

• Red: 7 students
• Blue: 8 students
• Green: 3 students
• Yellow: 2 students

The colour with the highest frequency is Blue (8 students), so Blue is the mode.

• 红色：7 名学生
• 蓝色：8 名学生
• 绿色：3 名学生
• 黄色：2 名学生

频数最高的颜色是蓝色（8 名学生），因此众数为蓝色。

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6. Interpreting a Bar Chart | 解读条形图

A bar chart shows the number of books read by five students in a month: Anna 5, Ben 3, Chloe 7, Daniel 4, Emily 6. Use the chart to answer: Who read the most books? How many more books did Chloe read than Ben?

一幅条形图显示了五名学生在一个月内阅读书籍的数量：Anna 5 本，Ben 3 本，Chloe 7 本，Daniel 4 本，Emily 6 本。请根据图表回答：谁读的书最多？Chloe 比 Ben 多读了多少本书？

From the bar chart, the tallest bar is for Chloe, with a frequency of 7. So Chloe read the most books. Ben read 3 books. The difference is 7 – 3 = 4. Chloe read 4 more books than Ben.

从条形图中可以看出，最高的条形对应 Chloe，频数为 7。因此 Chloe 读的书最多。Ben 读了 3 本书。两人的差值为 7 – 3 = 4。Chloe 比 Ben 多读了 4 本书。

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7. Pie Chart Angles and Interpretation | 饼图角度与解读

In a survey, 30 students choose their favourite fruit: Apple 10, Banana 12, Orange 8. Calculate the angle for each sector if the data is shown in a pie chart. Then state the fraction of students who chose Banana.

在一项调查中，30 名学生选择了自己最喜欢的水果：苹果 10 人，香蕉 12 人，橙子 8 人。如果要用饼图表示，请计算每个扇形的角度，并写出选择香蕉的学生所占的比例。

Total number of students = 30. Each student represents 360° ÷ 30 = 12°. Apple: 10 × 12° = 120°. Banana: 12 × 12° = 144°. Orange: 8 × 12° = 96°. The fraction for Banana is 12/30, which simplifies to 2/5.

学生总人数为 30。每名学生对应的角度为 360° ÷ 30 = 12°。苹果：10 × 12° = 120°。香蕉：12 × 12° = 144°。橙子：8 × 12° = 96°。选择香蕉的人数为 12/30，化简为 2/5。

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8. Comparing Data Sets Using Mean and Range | 利用平均数与极差比较数据

Two groups of students took the same test. Group A scored: 10, 12, 14, 16, 18. Group B scored: 13, 13, 14, 15, 15. Calculate the mean and range for each group. Which group performed more consistently?

两组学生参加了同一场测验。A 组分数为：10, 12, 14, 16, 18。B 组分数为：13, 13, 14, 15, 15。请分别计算每组分数的平均数和极差。哪一组的成绩更稳定？

Group A mean: (10+12+14+16+18) ÷ 5 = 70 ÷ 5 = 14. Range: 18 – 10 = 8. Group B mean: (13+13+14+15+15) ÷ 5 = 70 ÷ 5 = 14. Range: 15 – 13 = 2. Both groups have the same mean, but Group B has a much smaller range, indicating its scores are more consistent.

A 组平均数：(10+12+14+16+18) ÷ 5 = 70 ÷ 5 = 14。极差：18 – 10 = 8。B 组平均数：(13+13+14+15+15) ÷ 5 = 70 ÷ 5 = 14。极差：15 – 13 = 2。两组平均数相同，但 B 组的极差小得多，这表明 B 组的成绩更加稳定。

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9. Interpreting a Line Graph | 解读折线图

A line graph shows the monthly rainfall (in mm) from January to June: Jan 50, Feb 45, Mar 55, Apr 60, May 70, Jun 65. Describe the trend from January to May. Between which two consecutive months was the greatest increase in rainfall?

一幅折线图显示了一月至六月的月降雨量（单位：毫米）：一月 50，二月 45，三月 55，四月 60，五月 70，六月 65。请描述从一月到五月的趋势。在哪两个连续月份之间降雨量增长最大？

From January to May, the general trend is upward, though there is a slight dip in February. The greatest increase occurs between April (60 mm) and May (70 mm), with a rise of 10 mm. Other increases are 5 mm or less.

从一月到五月，整体趋势是上升的，尽管二月略有下降。降雨量增长最大的是四月（60 毫米）到五月（70 毫米），增长了 10 毫米。其他相邻月份的增长都不超过 5 毫米。

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10. Choosing the Right Average | 选择合适的平均数

A small company has five employees with annual salaries: £18,000, £20,000, £22,000, £24,000, and £26,000. The owner earns £120,000. If the owner’s salary is included, which measure of average — mean or median — better represents the typical salary? Explain why.

一家小公司有五名员工，年薪分别为：£18,000, £20,000, £22,000, £24,000, £26,000。老板的年薪为 £120,000。如果计入老板的薪水，平均数和中位数哪个更能代表典型的薪水？请解释原因。

Including the owner, the mean is (£18,000+£20,000+£22,000+£24,000+£26,000+£120,000) ÷ 6 = £230,000 ÷ 6 ≈ £38,333, which is much higher than most salaries. The median remains at £23,000 (middle of £22,000 and £24,000). The median is the better measure because it is not affected by the extreme value of £120,000 and gives a more realistic idea of a typical salary.

计入老板的薪水后，平均数为 (£18,000+£20,000+£22,000+£24,000+£26,000+£120,000) ÷ 6 = £230,000 ÷ 6 ≈ £38,333，远高于多数人的薪水。中位数则保持在 £23,000（£22,000 和 £24,000 的中间值）。中位数是更合适的度量，因为它不受极端值 £120,000 的影响，能更真实地反映典型的薪水水平。

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📚 Year 7 CAIE Statistics: Exam Techniques and Mark Schemes | Year 7 CAIE 统计：答题技巧与评分标准

Preparing for your Year 7 CAIE statistics exam involves more than just knowing the content—you must understand how marks are awarded and how to present your answers effectively. This guide covers the key exam techniques and explains the mark scheme so you can maximise your score. From drawing precise graphs to calculating averages and interpreting data, every detail counts.

为七年级 CAIE 统计考试做准备，不仅需要掌握知识内容，还必须了解评分方式以及如何有效地呈现答案。本指南涵盖关键的答题技巧，并解释评分标准，帮助你最大限度地提高分数。从绘制精确的图表到计算平均数和解读数据，每个细节都很重要。

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1. Understanding the Mark Scheme | 理解评分标准

In CAIE statistics exams, marks are divided into method marks (M), accuracy marks (A), and independent marks (B). Method marks reward you for using a correct approach, even if a calculation mistake leads to a wrong answer. Accuracy marks are for the correct final answer, but you can only get them if you have shown the right method or if the answer is independent. Independent marks are awarded for responses that do not need working, such as reading a value from a chart.

在 CAIE 统计考试中，分数分为方法分 (M)、准确分 (A) 和独立分 (B)。方法分奖励你使用了正确的方法，即使计算错误导致答案错误也能得分。准确分是针对最终答案正确而给予的，但通常只有展示了正确方法时才能获得。独立分是为不需要过程的答案而设，比如从图表中读取数值。

Examiners look for evidence of your understanding. A correct answer with no working may not earn full marks if the question requires method steps. Always show your calculations, even for simple questions. This technique increases your chance of gaining partial credit.

考官会寻找你理解题目的证据。如果题目要求方法步骤，没有过程的正确答案可能拿不到满分。始终展示你的计算过程，即使是简单的题目。这种技巧能增加获得部分分数的机会。

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2. Show All Working Clearly | 清晰展示计算过程

When finding an average like the mean, write the sum of all values first, then divide by the number of values. For example: (12 + 15 + 18 + 20) ÷ 4 = 65 ÷ 4 = 16.25. Writing each step earns method marks even if you mis-add.

在计算平均数（均值）时，先写出所有值的总和，再除以数值的个数。例如：(12 + 15 + 18 + 20) ÷ 4 = 65 ÷ 4 = 16.25。写出每一步骤可以赚取方法分，即使加法算错也能得分。

For median, write the sorted list: 3, 5, 7, 9, 12. The middle is 7. If even, write the two middle numbers and their average. Do not just write the answer; show the ordering step.

对于中位数，写出排序后的列表：3, 5, 7, 9, 12。中间是 7。如果总数是偶数，写出中间的两个数并计算它们的平均数。不要只写答案；要展示排序步骤。

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3. Include Units and Labels | 包含单位与标签

Many students lose marks by forgetting units in their answers. If the data is in hours, include ‘hours’ after your average. In graphs, always label the x-axis and y-axis with a clear description and units. A bar chart without axis labels cannot earn full marks.

许多学生因为忘记在答案中写单位而失分。如果数据是以小时为单位，请在平均数后面加上“小时”。在图表中，始终要给 x 轴和 y 轴添加清晰的描述和单位。没有轴标签的条形图是拿不到满分的。

For tables, add a header row and indicate totals clearly. Use footnotes or a title if needed. Consistent labelling shows the examiner you have communicated the data properly.

对于表格，要添加表头行，并清晰标明总和。如有必要可以使用脚注或标题。一致性的标签向考官展示了你正确地传达了数据。

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4. Draw Graphs Accurately | 准确绘制图表

In bar charts, bars must be of equal width and separated by equal gaps. Use a ruler and plot the correct height from the frequency table. Remember to write a title for the chart. Do not draw continuous bars for discrete data unless instructed.

在条形图中，条形宽度必须相等，条形之间间隔相等。使用直尺并根据频数

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📚 Year 7 CAIE Statistics: Exam Time Planning and Strategies | Year 7 CAIE 统计：备考时间规划与策略

Preparing for your Year 7 CAIE Statistics exam can be smooth and stress-free if you blend subject knowledge with a well-structured time plan. This guide provides practical strategies to organise your revision, master key topics, and approach the test with confidence.

如果你将学科知识与结构良好的时间规划相结合，备考Year 7 CAIE统计考试就可以变得轻松无压。本指南提供实用策略，帮助你组织复习、掌握核心主题并自信应对考试。

1. Understanding the Exam Structure and Syllabus | 了解考试结构与大纲

The Year 7 Statistics paper mainly consists of structured questions that test your ability to handle data and apply probability.

Year 7统计试卷主要由结构题构成，考查你处理数据和运用概率的能力。

Key topics include data collection methods, types of data, frequency tables, bar charts, pictograms, pie charts, mean, median, mode, range, and simple probability.

关键主题包括数据收集方法、数据类型、频率表、条形图、象形图、饼图、均值、中位数、众数、极差和简单概率。

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2. Creating a Long-Term Study Calendar | 制定长期学习日历

Start your preparation about 8-10 weeks before the exam. Divide the syllabus into weekly blocks and assign each week to a main topic.

大约在考前8-10周开始备考。将大纲分成每周模块，每周分配一个主要主题。

Use a wall planner or digital calendar to mark revision sessions, practice tests, and rest days. This helps you maintain a balanced pace without cramming.

使用挂历或电子日历标注复习时段、模拟测试和休息日。这能帮你保持均衡的节奏，避免临时抱佛脚。

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3. Mid-Term Review: 4-6 Weeks to Go | 中期回顾：考前4-6周

By this stage, you should have covered all major topics. Now focus on identifying weak areas through self-assessment quizzes or past questions.

到这个阶段，你应当已经覆盖所有主要主题。现在通过自测小测或历年试题找出薄弱环节。

Create a ‘trouble list’ of concepts you find difficult and allocate extra time to revise them with help from notes, videos, or a study partner.

制作一个你感到困难的概念”问题清单”，并借助笔记、视频或学习伙伴额外安排时间进行复习。

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4. Intensive Revision: The Final Fortnight | 强化复习：最后两周

Dedicate the last two weeks to timed practice papers. Simulate exam conditions to build speed and accuracy.

将最后两周用于限时练习卷。模拟考试环境以提升速度和准确度。

Review formulas and key definitions daily. Make flashcards for terms like ‘discrete data’, ‘continuous data’, and probability rules.

每天复习公式和关键定义。制作闪卡记忆”离散数据”、”连续数据”和概率规则等术语。

Focus on common mistakes: misreading scales on graphs, confusing mean with median, and forgetting to label diagrams.

关注常见错误：误读图上的刻度、混淆均值和中位数、忘记为图表添加标签。

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5. Mastering Data Collection and Representation | 掌握数据收集与呈现

Understand the difference between primary and secondary data. Primary data is collected first-hand through surveys or experiments.

理解原始数据与二手数据的区别。原始数据是通过调查或实验直接收集的。

Learn to design unbiased questions. A good questionnaire uses clear language and avoids leading questions, such as “Don’t you agree that…?”

学会设计公正的问题。一份好的问卷使用清晰的语言，避免引导性问题，例如”你不认为……吗？”。

For graphical representation, practise drawing and interpreting bar charts, pictograms, and pie charts. Remember that pie chart angles must add to 360°.

对于图形表示，练习绘制和解读条形图、象形图和饼图。记住饼图的角度总和必须为360°。

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6. Calculating and Interpreting Averages | 计算与解读平均数

The three measures of average are mean, median, and mode. The mean is the sum of all values divided by the number of values.

三种平均数度量是均值、中位数和众数。均值是所有数值之和除以数值的个数。

Mean = (sum of all data values) / number of values

均值 = 所有数据值之和 / 值的个数

The median is the middle value when data is ordered. If there are two middle values, take their mean.

中位数是数据排序后位于中间的值。如果有两个中间值，则取它们的均值。

The mode is the value that appears most often. A dataset may have no mode, one mode, or more than one mode.

众数是出现次数最多的值。一组数据可能没有众数、有一个众数或多个众数。

The range is the difference between the highest and lowest values and shows the spread of the data.

极差是最大值与最小值之差，显示数据的离散程度。

Range = highest value – lowest value

极差 = 最大值 – 最小值

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7. Introduction to Probability | 概率入门

Probability measures how likely an event is to happen, on a scale from 0 (impossible) to 1 (certain).

概率衡量事件发生的可能性，从0（不可能）到1（必然）的尺度上表示。

The probability of an event happening = number of favourable outcomes / total number of outcomes.

事件发生的概率 = 有利结果的数量 / 总结果的数量。

P(Event) = favourable outcomes / total outcomes

P(事件) = 有利结果数 / 总结果数

Practice listing outcomes for simple experiments, like rolling a die or flipping a coin, and using probability words: likely, unlikely, even chance.

练习列出简单实验的结果，如掷骰子或投硬币，并使用概率词汇：很可能、不太可能、等可能。

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8. Exam-Day Tactics for Success | 考试日成功策略

Read through the entire paper during the first few minutes. Identify the questions you are most confident about and tackle them first.

开始几分钟内通读全卷。找出你最有信心的题目并优先作答。

Manage your time by checking the marks allocated. Do not spend too long on a single question; move on and return later if needed.

通过查看配分来管理时间。不要在单个题目上花费过长时间；必要时先做后面的再回头。

Show all your working for calculations. Even if the final answer is wrong, you can earn method marks.

展示所有计算过程。即使最终答案错误，你仍可获得步骤分。

Check your graphs for labelled axes, correct scales, and accurate plotting. Use a ruler for straight lines.

检查图表，确保坐标轴有标签、刻度正确且描点准确。使用直尺画直线。

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📚 Cambridge Year 7 Statistics: The Ultimate International Competition Preparation Guide | 剑桥七年级统计：国际竞赛终极备战攻略

Competitions such as the UKMT Junior Mathematical Challenge, the AMC 8, and the Math Kangaroo often feature statistics questions that test your ability to collect, organize, and interpret data. This guide will help Year 7 students master the key statistical concepts and ace international contests.

许多国际数学竞赛，如UKMT少年数学挑战赛、AMC 8和袋鼠数学竞赛，都会考查学生收集、整理和解读数据的能力。本攻略将帮助七年级学生掌握核心统计概念，在国际赛事中脱颖而出。

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1. Understanding the Scope of Statistics in Competitions | 理解竞赛中的统计考查范围

International math competitions for Year 7 students typically include statistics questions under the ‘Data Handling’ strand. You might be asked to read and draw pictograms, bar charts, and pie charts, calculate averages, or solve probability puzzles. Understanding the examiners’ intentions is the first step to success.

七年级国际数学竞赛中的统计题目通常属于“数据处理”板块。你可能需要阅读和绘制象形图、条形图、饼图，计算平均数，或解决概率谜题。理解出题人的意图是成功的第一步。

Key topics that appear repeatedly include finding the mode from a frequency table, interpreting a compound bar chart, and using simple probability. Do not overlook the skill of designing a data collection sheet, as it occasionally appears.

反复出现的关键主题包括从频数表中找出众数、解读复合条形图以及运用简单概率。不要忽视设计数据收集表格的能力，这一考点偶尔也会出现。

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2. Data Types and Collection Methods | 数据类型与收集方法

In competitions, you may need to distinguish between qualitative and quantitative data, or discrete and continuous data. For example, ‘favourite colour’ is qualitative; ‘number of siblings’ is discrete quantitative. Recognising this helps you choose the right graph.

在竞赛中，你可能需要区分定性与定量数据，或离散与连续数据。例如，“最喜欢的颜色”是定性数据，“兄弟姐妹的数量”是离散定量数据。能够识别这些有助于你选择正确的图表。

A well-designed data collection sheet uses tally marks to record frequencies efficiently. In a contest setting, you might be given raw data and asked to complete a frequency table using tallies. Practice drawing neat tally marks with groups of five (like a gate: ||||).

一个设计良好的数据收集表使用计数标记高效地记录频数。在竞赛情景中，你可能会拿到原始数据并被要求用计数符号完成频数表。练习画出整洁的“五栏”计数标记（如“正”字或类似门形：||||）。

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3. Frequency Tables and Tally Marks | 频数表与计数标记

A frequency table lists each category or value alongside its count. When given a set of data, make sure you total the frequencies correctly — the sum should equal the number of data items. Many competition questions test this simple check.

频数表列出每个类别或数值及其计数。给定一组数据时，确保正确合计频数——总和应等于数据项的个数。许多竞赛题会测试这一简单的检查。

Sometimes you must find the mode directly from a frequency table. The mode is the category or value with the highest frequency. Avoid confusing it with the largest number in the category; it is simply the most common one.

有时你需要直接从频数表中找出众数。众数是频数最高的类别或数值。不要将其与类别中的最大数值相混淆；它只是最常见的那个。

Watch out for two categories having the same highest frequency; then the data can be bimodal, and you should list both modes.

注意两个类别可能具有相同的最高频数，那么数据是双峰的，你应该列出两个众数。

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4. Drawing and Interpreting Pictograms | 绘制和解读象形图

Pictograms use symbols to represent data. Each symbol stands for a certain number of items. Always check the key! If one smiley face equals 4 students, half a face stands for 2. Competition problems often test half symbols.

象形图用符号表示数据。每个符号代表一定数量的项。务必查看图例！如果一个笑脸代表4名学生，那么半个笑脸代表2名。竞赛题目常考半符号。

When drawing a pictogram, align your symbols neatly in rows or columns, and always write a clear key. If the frequency is not a multiple of the symbol value, use part of a symbol proportionally. Be precise in representing the value.

绘制象形图时，将符号整齐地排列成行或列，并始终写清楚图例。如果频数不是符号值的整数倍，按比例使用部分符号。要精确地表示数值。

Interpretation questions might ask: ‘How many more students chose apples than bananas?’ Subtract the frequencies correctly after reading the symbols; do not guess.

解读类问题可能会问：“选择苹果的学生比选择香蕉的学生多多少？”在读取符号后正确减去频数；不要猜测。

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5. Bar Charts and Compound Bar Charts | 条形图与复合条形图

A bar chart uses rectangular bars with heights proportional to frequencies. Ensure bars are of equal width and are spaced evenly. In a competition, you may need to construct a bar chart from a frequency table or vice versa.

条形图使用矩形条，高度与频数成正比。确保条宽度相等且间距均匀。在竞赛中，你可能需要从频数表构建条形图，或反过来。

Compound bar charts show two or more sub-categories within each main category using stacked or side-by-side bars. Read them carefully — the total height of a stacked bar is the sum of its parts. A typical question might ask for the difference between two sub-categories.

复合条形图使用堆叠或并排的条来展示每个主要类别中的两个或多个子类别。仔细阅读——堆叠条的总高度是其各部分之和。典型问题可能会问两个子类别之间的差异。

When interpreting bar charts, always read the scale on the vertical axis. One small square might represent 2, 5, or 10 units. Don’t assume it is always 1. Misreading the scale is a common error.

解读条形图时，一定要阅读纵轴上的刻度。一个小方格可能代表2、5或10个单位。不要总假设它是1。读错刻度是常见错误。

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6. Pie Charts and Proportional Reasoning | 饼图与比例思维

Pie charts display proportions. The total angle at the centre is 360°. To find the angle for a category, use the formula: angle = (frequency ÷ total frequency) × 360°. Competitions often test this calculation.

饼图显示比例。中心总角度为360°。求一个类别的角度，使用公式：角度 = (频数 ÷ 总频数) × 360°。竞赛中经常考查这一计算。

You may be asked to estimate the fraction or percentage represented by a sector. Practice recognising common angles: 90° is 1/4, 180° is 1/2, 120° is 1/3, and so on. This speeds up problem-solving.

你可能会被要求估计一个扇形代表的分数或百分比。练习识别常见角度：90°是1/4，180°是1/2，120°是1/3，等等。这可以加快解题速度。

Sometimes you must construct a pie chart from a frequency table. Use a protractor to measure angles accurately. Even a small error can make the chart look inconsistent. In competitions, marks are awarded for correct angles and labelling.

有时你需要从频数表构建饼图。使用量角器精确测量角度。即使小错误也会使图表看起来不一致。竞赛中，角度正确和标记完整会得到分数。

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7. Mean, Median, Mode, and Range | 均值、中位数、众数与极差

The mean is the average obtained by adding all values and dividing by the number of values. It is sensitive to extreme values (outliers). The median is the middle value when data are ordered; it is not affected by outliers. The mode is the most frequent value.

均值是通过将所有数值相加再除以数值个数得到的平均数。它对极端值（离群值）敏感。中位数是数据排序后的中间值；它不受离群值影响。众数是最常出现的值。

The range tells you how spread out the data are: range = largest value – smallest value. A small range means the data are clustered; a large range suggests wide variation. Competition questions may combine range with other averages.

极差告诉你数据的离散程度：极差 = 最大值 – 最小值。极差小意味着数据集中；极差大则表明差异很大。竞赛题目可能将极差与其他平均数结合起来考查。

When finding the median from a frequency table, you can list all data values or use cumulative frequency. For Year 7, listing is often acceptable. Ensure you have the correct total number and pick the middle value(s). If the total is even, average the two middle values.

从频数表中找中位数时，你可以列出所有数据值或使用累计频数。对于七年级学生，列举通常是可以接受的。确保总数正确，并挑选中间值。如果总数是偶数，取中间两个值的平均数。

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8. Introduction to Probability: Likelihood and Fractions | 概率入门：可能性与分数

Probability is a measure of how likely an event is to happen, expressed as a fraction, decimal, or percentage between 0 and 1. The probability of an impossible event is 0; a certain event is 1. In competitions, you’ll often use the formula: Probability = (number of favourable outcomes) / (total number of outcomes).

概率是对事件发生可能性的度量，用0到1之间的分数、小数或百分数表示。不可能事件的概率为0；必然事件的概率为1。竞赛中，你常会使用公式：概率 = (有利结果数) / (总结果数)。

For a fair six-sided dice, the probability of rolling a 4 is 1/6. Probabilities can also be expressed as equivalent fractions, decimals (≈0.167), or percentages (≈16.7%). Make sure you can convert between them quickly.

对于公平的六面骰子，掷出4的概率是1/6。概率也可以用等值分数、小数（≈0.167）或百分数（≈16.7%）表示。确保你能够快速进行转换。

Some competition problems involve finding the probability of ‘not’ an event. Use the complement rule: Probability(not A) = 1 – Probability(A). Practice this to save time.

一些竞赛问题涉及求“不”发生某事件的概率。使用补集规则：概率(非A) = 1 – 概率(A)。练习这个可以节省时间。

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9. Competition Questions Breakdown and Strategies | 竞赛真题精讲与解题策略

Let’s analyze a typical question: ‘The bar chart shows the number of pets owned by students in Year 7. 15 students have cats, 10 have dogs, 5 have rabbits. What is the probability that a randomly chosen student has a dog?’ Solution: total students = 15+10+5=30. Probability = 10/30 = 1/3.

我们来分析一道典型题目：“条形图显示了七年级学生拥有的宠物数量。15名学生养猫，10名养狗，5名养兔子。随机选择一名学生，他养狗的概率是多少？”解答：总学生数=30。概率=10/30=1/3。

Another example: ‘Find the mean of the numbers: 12, 15, 18, 21, 24.’ Sum = 90, divided by 5 gives 18. Notice the numbers are evenly spaced; the mean equals the middle value (median). This is a useful check.

另一个例子：“求这组数的均值：12, 15, 18, 21, 24。”总和=90，除以5得18。注意这些数字间隔均匀；均值等于中间值（中位数）。这是一个有用的检验方法。

When facing a tricky graph, underline key words and numbers. Write down what each axis represents. Always double-check the scale. If there are multiple bars per category, identify which one you need.

遇到棘手的图表

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📚 Year 7 Cambridge Statistics: Unit Test Mock Paper Walkthrough | Year 7 剑桥统计：单元测试模拟卷解析

This article walks you through a complete Cambridge Year 7 Statistics mock paper, covering typical questions on averages, charts, probability, and data collection. Each solution is explained step by step to help you revise effectively for your unit test.

本文为你逐题解析一份完整的剑桥 Year 7 统计模拟卷，涵盖平均值、图表、概率和数据收集等常见题型。每道题目的解答都配有逐步讲解，帮助你高效复习单元测试。

1. Overview of the Mock Paper | 模拟卷概述

The mock paper contains 10 questions, each testing a key skill from the Cambridge Year 7 Statistics curriculum. You will need to calculate mean, median, mode, and range; read bar charts, pie charts, and line graphs; understand basic probability; draw Venn diagrams; and use sample space diagrams.

这份模拟卷包含 10 道题，每道题考查剑桥 Year 7 统计课程中的一项关键技能。你需要计算平均值、中位数、众数和极差；阅读条形图、饼图和折线图；理解基础概率；绘制维恩图；以及使用样本空间图。

The total marks are 40, and the suggested time is 45 minutes. Let’s go through each question together.

试卷满分为 40 分，建议完成时间为 45 分钟。让我们一起来逐题分析。

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2. Question 1: Mean from a Frequency Table | 第1题：频率表求均值

The question gives the number of pets owned by 20 students in a frequency table. You are asked to calculate the mean number of pets.

题目给出 20 名学生拥有宠物数量的频率表。要求计算宠物的平均数。

First, multiply each number of pets by its frequency. Then add all the products. Finally, divide the total by the sum of frequencies.

首先，将每种宠物数量乘以其频数。然后，将所有乘积相加。最后，用总和除以频数的总和。

For example, if 0 pets (f=4), 1 pet (f=8), 2 pets (f=5), 3 pets (f=3), the total sum is 0×4 + 1×8 + 2×5 + 3×3 = 0+8+10+9 = 27. Mean = 27 ÷ 20 = 1.35 pets.

例如，如果有 0 只宠物（f=4），1 只（f=8），2 只（f=5），3 只（f=3），总和为 0×4 + 1×8 + 2×5 + 3×3 = 0+8+10+9 = 27。平均数 = 27 ÷ 20 = 1.35 只宠物。

Always check that the sum of frequencies matches the total number of data points.

记得检查频数总和是否与数据总数一致。

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3. Question 2: Interpreting a Bar Chart | 第2题：条形图解读

A bar chart shows the favourite sports of 30 pupils. You need to read frequencies correctly from the vertical axis and compare categories.

图中显示了 30 名学生最喜爱的运动。你需要从纵轴正确读取频数，并对类别进行比较。

Make sure you check the scale on the y-axis – sometimes it goes up in 2s, 5s, or 10s. Subtract to find how many more pupils prefer one sport than another.

一定要检查 y 轴上的刻度——有时每格代表 2、5 或 10。用减法计算喜欢一种运动比另一种多出多少人。

If football has frequency 12 and tennis has 7, then 5 more pupils prefer football. You might also be asked to write a conclusion, like ‘Football is the most popular sport’.

如果足球的频数是 12，网球是 7，那么喜欢足球的多了 5 人。你可能还需要写一条结论，例如“足球是最受欢迎的运动”。

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4. Question 3: Median and Mode | 第3题：中位数和众数

A list of scores is given: 8, 3, 5, 9, 5, 7, 10, 5, 6. You must find the mode and the median.

给出一组分数：8, 3, 5, 9, 5, 7, 10, 5, 6。要求找出众数和中位数。

The mode is the value that appears most often. Here, 5 appears three times, so mode = 5.

众数是出现次数最多的值。这里 5 出现了三次，所以众数 = 5。

For the median, first arrange the numbers in order: 3, 5, 5, 5, 6, 7, 8, 9, 10. The middle value of this 9-number list is the 5th value, which is 6. So median = 6.

求中位数时，先将数字按顺序排列：3, 5, 5, 5, 6, 7, 8, 9, 10。这组 9 个数的中间值是第 5 个，即 6。所以中位数 = 6。

If there are an even number of values, you must find the mean of the two middle numbers.

如果数据个数为偶数，必须求中间两个数的平均数。

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5. Question 4: Calculating the Range | 第4题：计算极差

The question provides a set of daily temperatures: 12 °C, 15 °C, 9 °C, 18 °C, 14 °C. Find the range.

题目给出了一组每日气温：12 °C, 15 °C, 9 °C, 18 °C, 14 °C。求极差。

Range = highest value – lowest value. Identify the maximum (18) and the minimum (9), then subtract: 18 – 9 = 9 °C.

极差 = 最大值 – 最小值。找出最大值（18）和最小值（9），然后相减：18 – 9 = 9 °C。

The range tells you how spread out the data are. A larger range means more variation.

极差表示数据的分散程度。极差越大，数据的波动范围就越大。

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6. Question 5: Pie Chart Angles | 第5题：饼图角度

You are told that in a survey of 40 students’ transport to school, 10 walk, 20 take the bus, and 10 cycle. Calculate the angle for each sector in a pie chart.

在一项关于 40 名学生上学交通方式的调查中，10 人步行，20 人乘公交，10 人骑自行车。请计算饼图中每个扇形的角度。

Total frequency = 40. The angle for one person = 360° ÷ 40 = 9°. Multiply each frequency by 9°.

总频数 = 40。每个人对应的角度 = 360° ÷ 40 = 9°。将每个频数乘以 9°。

• Walk: 10 × 9° = 90°
• Bus: 20 × 9° = 180°
• Cycle: 10 × 9° = 90°

Always check that the three angles sum to 360°: 90+180+90 = 360.

一定要检查三个角度之和是否为 360°：90+180+90 = 360。

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7. Question 6: Data Collection Methods | 第6题：数据收集方法

This question asks you to choose the best data collection method for a given situation: survey, observation, experiment, or using a secondary source.

本题要求你为所给情景选择最佳的数据收集方法：问卷、观察、实验或使用二手资料。

For example, to find out the number of cars passing a road, observation is suitable. To collect opinions on a new school lunch menu, a survey with a questionnaire is best.

例如，要了解通过某条路的汽车数量，适合使用观察法。要收集对新学校午餐菜单的意见，最好是使用问卷进行调查。

You must also design a suitable data collection sheet, including tally marks and clear categories. Make sure the categories do not overlap.

你还需要设计一份合适的数据收集表，包括划记标记和清晰的分类。确保类别之间没有重叠。

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8. Question 7: Basic Probability | 第7题：基础概率

A bag contains 3 red, 2 blue, and 5 green marbles. Find the probability of picking a red marble, and the probability of picking a marble that is not blue.

一个袋子装有 3 颗红色、2 颗蓝色和 5 颗绿色弹珠。求摸到红色弹珠的概率，以及摸到不是蓝色弹珠的概率。

Total marbles = 3+2+5 = 10. P(red) = 3/10. P(not blue) = (3+5)/10 = 8/10, which simplifies to 4/5.

弹珠总数 = 3+2+5 = 10。P(红色) = 3/10。P(非蓝色) = (3+5)/10 = 8/10，化简为 4/5。

Probability is always written as a fraction, decimal, or percentage between 0 and 1. In this test, fractions should be given in simplest form.

概率总是写成分数、小数或百分比，范围在 0 到 1 之间。本次测试中，分数应化为最简形式。

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9. Question 8: Venn Diagrams | 第8题：维恩图

In a class of 30 students, 18 study French, 15 study Spanish, and 8 study both. Draw a Venn diagram and find how many students study neither language.

在一个 30 名学生的班级中，18 人学习法语，15 人学习西班牙语，8 人两门都学。画出维恩图并求出两门语言都不学的学生人数。

Label the two overlapping circles. Place 8 in the intersection. For French only: 18 – 8 = 10. For Spanish only: 15 – 8 = 7. Total inside the circles = 10+8+7 = 25.

给两个重叠的圆圈做好标注。将 8 放在交集处。只学法语的人数：18 – 8 = 10。只学西班牙语的人数：15 – 8 = 7。圆圈内总人数 = 10+8+7 = 25。

Students studying neither = total class – 25 = 30 – 25 = 5. Place this number outside the circles.

两门都不学的学生 = 班级总数 – 25 = 30 – 25 = 5。将这个数字写在圆圈外面。

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10. Question 9: Line Graph Trends | 第9题：折线图趋势

A line graph shows the temperature in a town over 7 days. You must describe the trend and identify the day with the highest temperature.

折线图显示了一个小镇 7 天的气温。你需要描述变化趋势，并指出哪天温度最高。

Read the coordinates carefully. Days are on the horizontal axis, temperatures on the vertical axis. Use phrases like ‘increased rapidly’, ‘remained steady’, or ‘decreased slightly’ to describe trends between points.

仔细读取坐标点。横轴表示日期，纵轴表示温度。使用如“迅速上升”、“保持平稳”或“轻微下降”等短语来描述点与点之间的变化趋势。

Overall trend might be ‘the temperature rose from Monday to Friday, then fell at the weekend’. Always give specific values when asked.

整体趋势可能是“气温从周一到周五上升，然后周末下降”。在被要求时应给出具体数值。

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11. Question 10: Sample Space Diagrams | 第10题：样本空间图

Two fair six-sided dice are rolled. Draw a sample space diagram to show all possible outcomes, and find the probability that the sum of the two numbers is greater than 9.

掷两枚公平的六面骰子。画出样本空间图以显示所有可能的结果，并求两数之和大于 9 的概率。

Draw a 6 by 6 grid. List the outcomes (1,1), (1,2) … up to (6,6). There are 36 equally likely outcomes.

画一个 6×6 的网格。列出结果 (1,1), (1,2) …… 直到 (6,6)。共有 36 种等可能的结果。

Outcomes with sum > 9: (4,6), (5,5), (5,6), (6,4), (6,5), (6,6). There are 6 such outcomes. So probability = 6/36 = 1/6.

和大于 9 的结果有：(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)。共 6 种。因此概率 = 6/36 = 1/6。

Always simplify your fraction and double-count systematically to avoid missing any pairs.

始终化简分数，并系统地列举以免遗漏任何组合。

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📚 Common Misconceptions in Statistics and How to Correct Them | 统计常见误区与纠正方法

In Year 7 statistics, you meet new ways of describing and displaying data. Many students develop similar misunderstandings that can make the subject feel confusing. This article gathers the most common misconceptions – from reading graphs incorrectly to mixing up averages – and gives clear, step‑by‑step corrections that will help you think like a confident statistician.

在七年级统计课程中，你会接触到描述和展示数据的新方法。许多同学会产生相似的误解，让这门课感觉很难。本文整理了最常见的误区——从读错图表到混淆几种平均数——并给出清晰的分步纠正方法，帮助你建立统计学家的思维方式。

1. Confusing Mean, Median and Mode | 混淆平均数、中位数与众数

The mean is the sum of all values divided by how many there are. The median is the middle number when data are ordered. The mode is the value that appears most often. A typical mistake is to treat these three as interchangeable or to think the mean is always “the average” that best represents a set of numbers.

平均数（mean）是所有数值之和除以个数。中位数（median）是将数据排序后的中间值。众数（mode）是出现次数最多的数值。常见错误是把这三个概念混用，或者认为平均数总能最好地代表一组数据。

To choose the right measure, always ask: “Are there any extremely high or low values?” Outliers pull the mean up or down, so the median then gives a better idea of a typical value. The mode is most useful for non‑numerical data, such as favourite colours.

要选择合适的度量，先问自己：“数据中有极端高或低的值吗？”异常值会把平均数拉高或拉低，这时中位数更能反映典型值。众数最适合非数值型数据，如调查最喜欢的颜色。

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2. Reading Bar Charts Without Checking the Frequency Axis | 不看频率轴就读条形图

Students often glance at a bar chart and assume the tallest bar shows the largest frequency – but they forget to look at the scale on the vertical axis. The axis might not start at zero, or the intervals might be uneven, making differences appear larger or smaller than they really are.

同学们常常扫一眼条形图就认为最高的条形表示最大频数——却忘记检查纵轴的刻度。纵轴可能不是从零开始，或者间隔不均匀，使差异看起来比实际更大或更小。

Always put your finger on the axis, read the starting number, and note the step size. If the axis is broken or starts at a number higher than zero, be cautious – a bar that looks twice as tall might represent a much smaller difference in real numbers.

一定要用手指指着坐标轴，看清起始数字和步长。如果纵轴有断裂或起点大于零，就要小心——高度是另一条两倍的条形，在实际数字上可能相差很小。

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3. Ignoring Key Information in a Pictogram | 忽略象形图中的图例信息

A pictogram uses symbols to represent a fixed number of items. A frequent mistake is to count the symbols without checking what one symbol stands for. If one smiley face represents 4 people, 5 smiley faces do not mean 5 people – they mean 20.

象形图用图形符号表示固定数量的项目。常见错误是数完符号而没检查每个符号代表多少。如果一个笑脸代表 4 人，那么 5 个笑脸不是 5 人，而是 20 人。

Before interpreting a pictogram, find the key. Circle the key value and write it beside the chart. When a symbol is cut in half, use fractions of the key value. This small habit prevents large counting errors.

解读象形图前，先找到图例。把图例的值圈出来并写在图表旁边。当符号被切成一半时，要按图例值的分数来计算。这个小习惯可以避免很大的计数错误。

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4. Misjudging Proportions in Pie Charts | 误判饼图中的比例

Pie charts show parts of a whole, but the eye is not good at comparing angles precisely. Many students guess that a slice is about 50% when it is actually only 30%, simply because it “looks big”. A common error is also forgetting that all slices together must add up to 100%.

饼图展示整体中的部分，但人眼不擅长精确比较角度。许多学生会凭感觉说某个扇形约占 50%，而实际只有 30%，就因为“看起来大”。另一个常见错误是忘记所有扇形总和必须为 100%。

Use the angle at the centre: 360° represents 100%. If you know the angle, divide it by 3.6 to get the percentage. For a rough check, compare each slice with a quarter (90°) or a half (180°) to ground your estimate.

利用圆心角：360° 代表 100%。如果知道了角度，除以 3.6 就得到百分比。做粗略检验时，可以跟四分之一（90°）或一半（180°）比较，让估算有据可依。

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5. Treating a Sample as the Whole Population | 把样本当作全部总体

When we take a survey, we usually ask a sample of people, not the whole population. A misconception is to think the results of a small survey apply exactly to everyone. For example, asking 10 friends about their favourite snack does not tell you what all Year 7 students in the country prefer.

做调查时，我们通常调查一组样本，而不是全部总体。误以为一个小调查的结果精确适用于所有人，这会出问题。例如，问 10 位朋友最喜欢什么零食，并不能代表全国七年级学生的喜好。

A good sample is large enough and chosen fairly, without bias. When reading survey results, always ask: “Who was asked, and how were they chosen?” If the sample is too small or only from one group, the conclusion is not reliable for the whole population.

好的样本要足够大、选用方式公正无偏。读调查结果时，永远要问：“问了谁？是怎么选出来的？”如果样本太小或者只来自某一个群组，那么结论对整个总体并不可靠。

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6. Thinking “Random” Means “Evenly Spread” | 以为“随机”就是“均匀分布”

In Year 7, you learn about randomness in dice rolls, coin flips, or picking a card. A widespread misconception is that random outcomes should look evenly distributed in a small number of trials. Many learners expect that after three heads in a row, a tail is “due”.

在七年级，你会学到掷骰子、抛硬币或抽牌中的随机性。一个普遍误解是认为在少量试验中，随机结果应该看起来均匀分布。很多同学会期望：连续三次正面后，反面该“出来了”。

Each roll or flip is independent – the coin has no memory. In the short term, any pattern is possible. Only when you repeat the experiment many hundreds of times does the frequency settle close to the theoretical probability. Remind yourself: “Random is lumpy, not smooth.”

每一次掷或抛都是独立的——硬币没有记忆。短期来看，任何模式都可能出现。只有当你重复成百上千次试验，频率才会接近理论概率。提醒自己：“随机是疙瘩状的，不是平滑的。”

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7. The Gambler’s Fallacy in Probability | 概率中的赌徒谬误

After observing a streak of outcomes, someone might think the opposite result becomes more likely. This belief is called the gambler’s fallacy. For example, if a spinner lands on red five times in a row, a student might predict that blue is “overdue” next time.

观察到一连串结果后，有人可能认为反面结果变得更有可能。这种想法叫做赌徒谬误。例如，如果转盘连续五次停在红色，学生可能会预测下一次蓝色该“来了”。

Probability does not compensate for past events. If each colour is equally likely, the chance of blue on the next spin remains the same, regardless of the previous spins. The correct thinking is: “Past outcomes do not change the probability of future independent events.”

概率不会为过去的事件“补偿”。如果每种颜色发生的可能性相等，那么下一次转到蓝色的概率始终保持不变，与之前的转盘结果无关。正确的思路是：“过去的结果不会改变未来独立事件的概率。”

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8. Misreading Two‑Way Tables | 错误解读双向表

Two‑way tables organise data by two categories, such as gender and favourite sport. A common error is to look at a single number inside the table and treat it as a total, without checking the row and column headings. Another mistake is to add frequencies incorrectly when finding totals.

双向表按两个类别整理数据，如性别和喜欢的运动。常见错误是只看表中的一个数字，就把它当作总计，而没有核对行与列的标题。另一个错误是求总数时把频数加错。

Before reading a two‑way table, place a ruler under the row and another beside the column you are interested in. The intersection gives the joint frequency only for those two categories. Always check the marginal totals – the “Total” row and column – to confirm your addition.

读双向表之前，用一把尺子放在你关注的行下方，另一把尺子放在列旁边。交叉处的数字只是这两个类别的联合频数。永远要检查边际总和——“总计”行和列——来确认你的加法是否正确。

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9. Confusing Correlation with Causation | 把相关关系当作因果关系

When two sets of data move together – like ice cream sales and sunglasses sales – we say they are correlated. A Year 7 misconception is to jump to the conclusion that one causes the other. Buying ice cream does not cause people to buy sunglasses; a third factor, sunny weather, influences both.

当两组数据一起变动——例如冰淇淋销量和太阳镜销量——我们说它们相关。七年级的常见误区是直接下结论认为一个导致另一个。买冰淇淋并不会导致人们买太阳镜；第三个因素——晴朗的天气——同时影响了两者。

Whenever you see a pattern on a scatter graph or read about linked trends, ask: “Is there a hidden variable that could explain both?” Only a controlled experiment, where you change one thing and keep everything else the same, can suggest causation.

每当你看到散点图上的规律或读到关联趋势时，问自己：“是否存在一个隐藏变量可以解释两者？”只有控制实验——改变一个因素并保持其他不变——才能提示因果关系。

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10. Forgetting to Divide by the Correct Total When Calculating the Mean | 计算平均数时忘记除以正确的总数

When finding the mean, some students add up the numbers but then divide by the wrong count – perhaps they use the number of categories instead of the number of data pieces. Another slip is to leave out zero values, as if they don’t count as data points.

计算平均数时，有的同学把数字加起来，却除以了错误的数目——可能用了类别个数，而非数据个数。另一种疏忽是漏掉零值，仿佛零不算数据点。

Write the total sum clearly, then underneath write “there are ___ pieces of data”. Count slowly, including every zero. The division is sum ÷ count. For example, the mean of 5, 0, 8, 2 is (5+0+8+2) ÷ 4 = 3.75, not 15 ÷ 3 = 5.

把总和清楚地写下来，然后在下面写“共有___个数据”。慢慢数，包括每个零。除法就是总和 ÷ 个数。例如，5, 0, 8, 2 的平均数是 (5+0+8+2) ÷ 4 = 3.75，而不是 15 ÷ 3 = 5。

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11. Ignoring the Effect of Outliers on the Mean | 忽略异常值对平均数的影响

An outlier is a value far away from the rest of the data. Many learners calculate the mean and stop, without noticing that one extreme salary or one extremely tall student has pulled the mean up. They then use that inflated mean to describe the whole set, which can be misleading.

异常值是与其余数据相距很远的数值。很多同学算出平均数就停步，没注意到一个极高薪资或一个极高的学生身高已经拉高了平均数。然后他们用那个偏高的平均数来描述整组数据，这可能产生误导。

After finding the mean, compare it with the median. If the mean is quite different from the median, an outlier is probably present. In those cases, report both measures and mention the outlier, so your summary is honest and accurate.

求出平均数后，跟中位数进行比较。如果平均数与中位数相差较大，很可能存在异常值。在这种情况下，同时报告两个度量并提及异常值，这样你的总结才诚实而准确。

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12. Believing a Graph “Proves” a Claim | 相信图表能“证明”一个说法

Statistics can be presented in ways that exaggerate or disguise the truth. A common misconception is to accept any chart at face value. For example, a line graph with a dramatic upward slope may use a short time period or a very compressed horizontal scale, making a small change look like a huge increase.

统计数据可以用夸大或掩盖真相的方式呈现。常见的误区是全盘接受任何图表。例如，一条陡峭上升的折线图可能使用了很短的时间段，或者水平轴被压得很紧，让一个很小的变化看起来像巨大的增长。

Become a critical reader of graphs: check the axes, the scale, the title, and the source of the data. Ask: “Does the title match what the graph actually shows?” and “Who collected this data, and why?” Skepticism is a healthy tool in statistics.

要成为图表的批判性读者：检查坐标轴、刻度、标题和数据来源。问自己：“标题和图表实际展示的内容一致吗？”以及“谁收集了这些数据，为什么？”怀疑精神是统计学中一个健康的工具。

Published by TutorHao | Statistics Revision Series | aleveler.com

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📚 Year 7 Cambridge Statistics: Top Scorer’s Secrets | Year 7 剑桥统计：学霸高分经验分享

Scoring top marks in Year 7 Cambridge Statistics is not about cramming formulas the night before the test — it’s about understanding how data tells a story. Many students see numbers and panic, but with the right habits you can master every topic from bar charts to probability experiments. Here I’ll share the exact methods that helped me consistently achieve above 90%, so you can build confidence and enjoy the subject.

在 Year 7 剑桥统计考试中拿高分，不是考前熬夜背公式，而是理解数据如何讲故事。很多同学一看到数字就慌，但只要养成正确习惯，从条形图到概率实验你都能轻松掌握。我会分享自己稳定拿到 90% 以上成绩的方法，帮你建立信心、真正爱上这门课。

1. Build a Data Vocabulary from Day One | 从第一天起建立数据词汇表

Every statistics question begins with words like ‘discrete’, ‘continuous’, ‘frequency’ or ‘outlier’. If you have to stop and guess their meaning, you lose time and accuracy. I kept a small notebook where I wrote each new term with its definition and an example — for instance, ‘discrete data: counted items (e.g. number of pets)’ vs ‘continuous data: measured values (e.g. height)’. Before long, I could read a question and immediately know what the examiner wanted.

每道统计题都以“离散”、“连续”、“频数”或“异常值”这类词开头。如果做题时还要停下来猜词义，不仅浪费时间还容易出错。我准备了一本小笔记本，把每个新术语、定义和例子都记下来——比如“离散数据：计数得到的数据（如宠物数量）”，“连续数据：测量得到的数据（如身高）”。很快我就能一眼看懂题目要求。

2. Master Tally Charts and Frequency Tables First | 先彻底掌握划记表和频数表

Most Year 7 topics — mean, mode, bar charts — depend on a tidy frequency table. Many marks are lost because students miscount or forget to include the total. I started every problem by drawing a three‑column table: ‘Data Value’, ‘Tally’ and ‘Frequency’. When collecting data or reading a list, I always crossed off items as I tallied. This simple habit cut my silly mistakes to nearly zero.

Year 7 的大多数知识点——平均数、众数、条形图——都依赖一张整洁的频数表。很多失分是因为学生数错或忘记写合计。我每次做题都先画一个三列表：“数据值”、“划记”、“频数”。处理一组数据时，一边划记一边划掉已计的数。这个简单习惯让我的粗心错误几乎降为零。

3. Treat the Mean, Median and Mode as a Trio | 把平均数、中位数和众数当作三兄弟来学

Instead of learning them separately, I compared mean, median and mode on the same small data set every time I revised. For example, with 3, 5, 5, 7, 10: the mean = (3+5+5+7+10) ÷ 5 = 6, the median is 5 (the middle number), and the mode is 5 (most frequent). Writing them side by side helped me see that the mean is pulled by extremes, while the median resists them. In the exam, I always checked: “Does my answer make sense with the data?”

我不是孤立地学，而是每次复习都把平均数、中位数和众数放在同一小组数据中对比。比如对 3,5,5,7,10：平均数=(3+5+5+7+10)÷5=6，中位数是5（中间那个），众数是5（出现最多的）。并排比较让我发现平均数会被极端值拉偏，而中位数比较“抗干扰”。考试时我总会自问：“我的答案和数据合得拢吗？”

4. Read Bar Charts, Not Just Draw Them | 不止会画条形图，更要读懂它

Many students can draw a neat bar chart but struggle when asked “How many more red cars than blue cars?” or “What fraction of the total were trucks?” I trained myself to treat a bar chart like a picture puzzle: first scan the axes labels, check the scale (does it start at zero?), then read the exact frequency from the top of each bar. I always wrote the frequencies above the bars before answering comparative questions.

很多同学能画出规整的条形图，但遇到“红色汽车比蓝色汽车多多少辆？”或“卡车占总数的几分之几？”就犯难。我训练自己把条形图当成图形谜题：先扫一眼坐标轴标签、检查刻度（起点是零吗？），再准确地从柱顶读取频数。回答比较型问题之前，我习惯先把每个柱子的频数标在柱顶。

5. Use a Step‑by‑Step Script for Pie Charts | 画饼图套用分步“剧本”

Pie chart questions often ask you to convert frequencies into angles by calculating (frequency ÷ total) × 360°. I created a mental script: (Step 1) Find the total frequency. (Step 2) For each category, divide its frequency by the total. (Step 3) Multiply by 360. (Step 4) Use a protractor to draw the angle. I practised this with a protractor and compass, checking that all my angles summed to 360°. On the exam, a quick angle‑sum check saved me from careless errors.

饼图题常要求把频数转换为角度，用（频数÷总数）×360°。我自编了一套心法：(第1步) 求总频数。(第2步) 每个类别用它的频数除以总数。(第3步) 乘以360。(第4步) 用量角器画出该角度。我反复用量角器和圆规练习，并检查所有角度加起来是不是360°。考场上快速验算角度和，让我躲过了粗心扣分。

6. Turn Everyday Situations into Probability Practice | 把日常情景变成概率练习

Probability was the most fun because I turned it into a game. Whenever I saw a dice, a spinner, a bag of coloured counters in a textbook, I wrote the sample space. For two dice, I drew a 6×6 grid. I memorised the probability scale from 0 (impossible) to 1 (certain) and used the formula P(event) = number of favourable outcomes ÷ total number of outcomes. I also practised with words like ‘even chance’, ‘likely’, ‘unlikely’ — Cambridge questions love mixing words and numbers.

概率最有趣，因为我把它变成了游戏。只要看到骰子、转盘、袋子里有彩色筹码，我就写下样本空间。对于两个骰子，我会画一个 6×6 的网格。我熟记概率标尺从 0（不可能）到 1（一定），并套用公式 P(事件)=有利结果数÷总结果数。我还练习“均匀机会”“很可能”“不太可能”这些词语——剑桥考题特别喜欢把文字和数字混在一起出。

7. Predict the Question Before Doing the Calculation | 先预测题目再动笔计算

Before picking up my pencil, I spent 15 seconds predicting a reasonable answer. If the data range was 10–50, the mean had to fall inside, not 2 or 300. If a pie chart category was huge, its angle had to be far larger than 90°. This “range check” caught so many button‑press errors. In statistics, common sense is your best proofread tool.

动笔之前，我会花 15 秒预测一个合理答案。如果数据范围是 10–50，平均数应该落在这个区间，不可能是 2 或 300。如果饼图里某个类别很大，它的角度一定远大于 90°。这种“范围检验”抓住了无数次计算器按错的错误。在统计中，常识就是你最好的校对工具。

8. Write Explanations That a Classmate Could Follow | 写出同学也能看懂的解题步骤

Cambridge marks not only the final answer but also your working. I imagined explaining my steps to a friend who missed the lesson. For a mean calculation, I wrote: “Sum = 12+18+15 = 45; Number of values = 3; Mean = 45 ÷ 3 = 15.” For a bar chart conclusion, I wrote: “The tallest bar is Green, with frequency 22, so green is the most popular.” Clear working earns method marks even if the final answer slips.

剑桥考试不只扣答案，也会给步骤分。我假想自己在给一位缺课的同学讲题。算平均数时我写：“总和=12+18+15=45；数值个数=3；平均数=45÷3=15。”分析条形图时写：“最高的柱子是绿色，频数为22，所以绿色最受欢迎。”清晰的步骤万一最终答案有误，还能保住方法分。

9. Revise with Past Questions and a Mistakes Diary | 用真题和错题本复习

I collected five Cambridge Year 7 statistics worksheets and past paper snippets. Under exam conditions, I timed myself: about 1 minute per mark. After marking, every mistake went into a colour‑coded diary — red for concept errors (e.g. confusing mean and median), blue for silly slips (e.g. missing a tally). Revisiting just those points before the test boosted my score more than rereading the textbook.

我收集了五套剑桥 Year 7 统计练习题和部分真题。模拟考试环境下计时：大约 1 分钟做 1 分的题。批改后，每个错误都分类记到错题本里——红色代表概念错误（如混淆平均数和中位数），蓝色代表粗心失误（如漏记一笔划记）。考前只复习这些点，提分效果远比重读课本好。

10. Stay Curious and Make Statistics Your Superpower | 保持好奇，让统计变成你的超能力

Beyond grades, statistics helps you understand the world — from sports averages to weather forecasts. I challenged myself to spot misleading graphs in news articles or calculate the mean of my daily screen time. That genuine interest showed in my exam answers because I could connect numbers to real meaning, not just follow rules. Once you make that shift, top scores come naturally.

除了分数，统计还能帮你理解世界——从体育平均数据到天气预报。我会挑战自己去发现新闻报道中误导性的图表，或者算算自己每天的屏幕使用时间平均数。这种真实的好奇心会体现在考卷答案里，因为我能把数字和实际意义联系起来，而不是死套规则。一旦完成这种转变，高分自然随之而来。

Published by TutorHao | Statistics Revision Series | aleveler.com

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📚 Year 7 Cambridge Statistics: Core Concepts Review | Year 7 剑桥统计：核心知识点梳理

Statistics helps us make sense of the world by turning raw numbers into clear pictures and useful summaries. In Year 7 Cambridge Mathematics, you learn the core skills of collecting, displaying and interpreting data. This article revisits all the key ideas you need to master, from types of data to averages and range, giving you a solid foundation for future studies.

统计学通过将原始数字转化为清晰的图表和有用的总结，帮助我们理解世界。在 Year 7 剑桥数学课程中，你将学习收集、展示和解读数据的基本技能。本文回顾所有你需要掌握的核心概念，从数据类型到平均数和极差，为今后的学习打下坚实基础。

1. What is Statistics? | 什么是统计？

Statistics is the science of collecting, organising, presenting, analysing and interpreting data. It allows us to answer questions, spot trends and make informed decisions in everyday life, from weather forecasts to sports performance.

统计学是一门收集、整理、展示、分析和解释数据的科学。它让我们能够回答问题、发现趋势并做出明智的决策，无论是天气预报还是体育表现分析，都离不开统计。

In Year 7, you focus on small data sets that you can manage by hand. The aim is to understand how data is handled honestly and how to draw sensible conclusions without being misled by charts or numbers.

在 Year 7，你主要处理可以手工管理的小型数据集。目的是理解如何诚实地处理数据，以及如何得出合理的结论而不被图表或数字误导。

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2. Types of Data | 数据类型

Data can be qualitative or quantitative. Qualitative data describes qualities or categories that cannot be measured with numbers, such as favourite colour, eye colour or type of pet.

数据可以分为定性数据和定量数据。定性数据描述无法用数字测量的性质或类别，例如最喜欢的颜色、眼睛颜色或宠物种类。

Quantitative data consists of numerical values that can be counted or measured. Quantitative data is further split into discrete data, which can only take certain fixed values (like the number of students in a class), and continuous data, which can take any value within a range (like height or temperature).

定量数据由可计数或可测量的数值组成。定量数据又分为离散数据和连续数据。离散数据只能取某些固定的值（如班级学生人数），连续数据可以在一个范围内取任意值（如身高或温度）。

Recognising the type of data is the first step in choosing the right chart and the most suitable average later.

识别数据类型是之后选择合适图表和适当平均数的第一步。

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3. Collecting Data | 收集数据

Data can be collected through surveys, questionnaires, observations or experiments. A well-designed data collection sheet or tally chart helps you record information systematically and avoid mistakes.

数据可以通过调查、问卷、观察或实验来收集。一张设计良好的数据记录表或计数表可以帮助你有条理地记录信息，避免错误。

When designing a questionnaire, questions should be clear, unbiased and easy to answer. For example, asking ‘How many hours of sport do you do each week?’ is better than a vague ‘Do you like sport?’ because the first gives quantitative data that is much easier to analyse.

在设计问卷时，问题应当清晰、无偏向且容易回答。例如，问“你每周运动多少小时？”比含糊地问“你喜欢运动吗？”更好，因为前者能得到更容易分析的定量数据。

In Year 7, you usually work with primary data you have collected yourself or secondary data from newspapers and books. Understanding where data comes from is essential for judging how reliable it is.

在 Year 7，你通常使用自己收集的一手数据或来自报纸和书籍的二手数据。了解数据的来源对于判断其可靠性至关重要。

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4. Frequency Tables | 频数表

A frequency table lists each data value or category and shows how many times it occurs (its frequency). Tally marks are commonly used to count while collecting data, with every fifth mark drawn diagonally to make groups of five easy to count.

频数表列出每个数据值或类别，并显示它出现的次数（即频数）。在收集数据时通常使用计数符号，每第五个标记画成斜线，以便五个一组计数。

For example, a survey of favourite fruits might produce a frequency table with ‘Apple’ having tally marks |||| || for a frequency of 7, and ‘Banana’ having ||| for a frequency of 3. A frequency table quickly organises raw data so you can see patterns and calculate totals.

例如，一项关于最喜欢水果的调查可能产生一张频数表，其中“苹果”的计数符号为 |||| ||，表示频数为 7，“香蕉”为 |||，频数为 3。频数表能快速整理原始数据，让你看到规律并计算总数。

Frequency tables can also be used to construct grouped frequency tables for continuous data, though in Year 7 you mostly work with ungrouped discrete data.

频数表也可用于为连续数据构建分组频数表，不过在 Year 7 你主要处理不分组的离散数据。

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5. Bar Charts | 条形图

A bar chart displays categorical data with rectangular bars. The height or length of each bar represents the frequency of that category. Bars must be of equal width and there should be equal gaps between them to show that the categories are separate.

条形图用矩形长条展示分类数据。每个长条的高度或长度代表该类别的频数。长条必须等宽，且长条之间应有相等的间距，以表明类别是分开的。

You label each axis clearly: the horizontal axis shows the categories, and the vertical axis shows the frequency. The scale on the vertical axis must start at zero and increase in equal steps, or the chart can become misleading.

你需要清晰地标记每个坐标轴：横轴显示类别，纵轴显示频数。纵轴的刻度必须从零开始并以等步长增加，否则图表可能会产生误导。

Bar charts make it easy to compare frequencies at a glance. For instance, a bar chart of pet ownership shows immediately which pet is most and least popular.

条形图能够让人一目了然地比较频数。例如，宠物拥有情况的条形图能立即显示哪种宠物最受欢迎、哪种最不受欢迎。

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6. Pictograms | 象形图

A pictogram uses small pictures or symbols to represent a certain number of items. A key is essential to tell the reader what each symbol stands for, for example one book symbol = 5 books read.

象形图使用小图片或符号来代表一定数量的项目。图例是必不可少的，它告诉读者每个符号代表什么，例如一个书本符号 = 5 本已读书籍。

When drawing a pictogram, symbols must be the same size and spaced evenly. If a frequency is not an exact multiple of the key value, you may show a part of a symbol, like half a book to represent 2.5 books rounded appropriately.

绘制象形图时，符号必须大小相同且均匀排列。如果某个频数不是图例数值的整数倍，你可以展示部分符号，比如用半个书本符号代表适当取整后的 2.5 本书。

Pictograms are visually appealing and useful for making data more engaging, but they can be less precise than bar charts when exact comparisons are needed.

象形图在视觉上很有吸引力，有助于让数据更生动有趣，但在需要精确比较时，它的精度可能不如条形图。

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7. Line Graphs | 折线图

A line graph is used to show how a quantity changes over time or across ordered categories. Data points are plotted and connected with straight line segments to reveal trends.

折线图用于显示一个量随时间或有序类别的变化。将数据点描出并用直线段连接起来，以揭示变化趋势。

The horizontal axis usually represents time (such as days, months or years), and the vertical axis represents the variable being measured. You must choose a sensible scale that spreads the data across the graph and makes trends visible.

横轴通常表示时间（如天、月或年），纵轴表示被测量的变量。你需要选择合理的刻度，让数据点分布在图上，使趋势清晰可见。

For example, a line graph of daily maximum temperature over a week can show whether the weather is warming or cooling. Line graphs are not suitable for categorical data that has no natural order.

例如，一周内每日最高气温的折线图可以显示天气是在变暖还是变冷。折线图不适合用于没有自然顺序的分类数据。

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8. Pie Charts | 饼图

A pie chart displays data as sectors of a circle, where each sector represents a category’s proportion of the whole. The size of each sector is determined by its angle, calculated as (frequency / total) × 360°.

饼图将数据展示为圆中的扇形，每个扇形代表一个类别在整体中所占的比例。每个扇形的大小由其角度决定，计算公式为 (频数 ÷ 总数) × 360°。

Pie charts are excellent for showing relative shares, such as how a budget is split or the composition of a class by eye colour. All sectors together must add up to 360°, and percentages can be added to help interpretation.

饼图非常适合于展示相对份额，例如预算如何分配，或按眼睛颜色划分的班级构成。所有扇形加起来必须等于 360°，并且可以加上百分比以帮助理解。

In Year 7, you learn to draw simple pie charts using a protractor and compass, and to interpret given charts by working backwards from angles to frequencies.

在 Year 7，你将学习使用量角器和圆规绘制简单的饼图，并学会通过从角度反推频数来解读给定的饼图。

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9. Mean (Average) | 平均数

The mean is the most common measure of average. It is calculated by adding up all the data values and then dividing by the number of values.

Mean = (sum of all values) ÷ (number of values)

平均数是衡量集中趋势最常用的指标。计算方法是：将所有数据值相加，再除以数据的个数。

平均数 = 所有数值之和 ÷ 数值个数

The mean gives a single number that represents the entire data set. However, it can be heavily influenced by unusually large or small values, called outliers. If a data set contains an outlier, the mean might not give a typical picture.

平均数是一个能代表整个数据集的单一数值。但它可能受到异常大或异常小的值（即离群值）的严重影响。如果数据集中含有离群值，平均数可能无法反映典型情况。

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10. Median | 中位数

The median is the middle value when the data is arranged in order from smallest to largest. For an odd number of values, the median is the exact middle value. For an even number of values, it is the mean of the two middle values.

中位数是将数据从小到大排列后位于中间的值。如果数据个数为奇数，中位数就是正中间的那个值；如果数据个数为偶数，则中位数是中间两个数的平均数。

For example, in the set 2, 3, 5, 7, 8 the median is 5. In the set 2, 3, 5, 7, 8, 10, the median is (5 + 7) ÷ 2 = 6. The median is not affected by outliers, so it often describes the typical value better when data is skewed.

例如，在数据集 2, 3, 5, 7, 8 中，中位数是 5。在数据集 2, 3, 5, 7, 8, 10 中，中位数是 (5 + 7) ÷ 2 = 6。中位数不受离群值影响，因此当数据分布偏斜时，它通常能更好地描述典型值。

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11. Mode | 众数

The mode is the value that appears most often in a data set. There can be one mode, more than one mode (bimodal or multimodal), or no mode at all if all values occur with the same frequency.

众数是数据集中出现次数最多的值。可以有一个众数、多个众数（双众数或多众数），或者如果所有值出现次数相同，则没有众数。

The mode is the only measure of average that can be used for qualitative data, such as finding the most common favourite colour. It is easy to spot from a frequency table or bar chart.

众数是唯一可以用于定性数据的平均数指标，例如找出最常见的最喜欢的颜色。它很容易从频数表或条形图中发现。

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12. Range | 极差

The range is a simple measure of how spread out the data is. It is calculated by subtracting the smallest value from the largest value.

Range = largest value – smallest value

极差是衡量数据分散程度的一种简单指标。计算方法是用最大值减去最小值。

极差 = 最大值 – 最小值

A larger range indicates that the data values are more spread out, while a smaller range suggests they are closely bunched together. Used alongside the mean or median, the range helps describe the consistency of a data set.

极差较大表明数据值更加分散，极差较小则表明数据值紧密聚集。与平均数或中位数一起使用时，极差有助于描述数据集的一致性。

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Published by TutorHao | Statistics Revision Series | aleveler.com

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📚 Year 7 Cambridge Statistics: Comparing UK University Entry Requirements | 英国大学申请要求对照

Statistics is a powerful tool that helps us make sense of data. In everyday life, we use statistics to compare options, spot trends and make informed decisions. One practical example is comparing the entry requirements of different UK universities. By collecting and analysing admission data, students can better understand what grades they need and how universities differ. This topic introduces you to key Year 7 statistical skills – collecting data, making frequency tables, drawing bar charts and calculating averages and range – all through the lens of real university offers.

统计学是一种强大的工具，能帮助我们理解数据。在日常生活中，我们用统计学来比较各种选项、发现趋势并做出明智的决定。一个实际的例子是比较不同英国大学的入学要求。通过收集和分析录取数据，学生可以更好地了解他们需要什么样的成绩，以及各大学之间的差异。本主题将通过真实的大学录取数据，向你介绍英国7年级统计的关键技能——收集数据、制作频率表、绘制柱状图以及计算平均数和范围。

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1. Understanding Statistics | 认识统计

Statistics is the science of collecting, organising, presenting and interpreting data. In Year 7, you will learn how to gather information, summarise it in tables and graphs, and use measures such as the mean, median, mode and range to describe the data. These skills are not just for exams – they are used by universities, employers and researchers every day.

统计学是收集、整理、展示和解读数据的科学。在7年级，你将学习如何收集信息，用表格和图表进行总结，并使用平均数、中位数、众数和范围等度量来描述数据。这些技能不仅仅用于考试——大学、雇主和研究人员每天都在使用它们。

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2. Collecting University Entry Data | 收集大学申请数据

To compare UK university entry requirements, we first gathered the typical A-level offers for popular courses at ten well-known universities. Since A-level grades come as letters, we converted each offer into a numerical UCAS tariff point total: A* = 56, A = 48, B = 40, C = 32, D = 24, E = 16. This gives us a consistent set of numbers to analyse. The table below shows our data set.

为了比较英国大学的入学要求，我们首先收集了十所知名大学热门课程的典型A-level录取条件。因为A-level成绩是用字母表示的，我们将每个录取条件转换为数值型的UCAS积分总和：A* = 56分，A = 48分，B = 40分，C = 32分，D = 24分，E = 16分。这样我们就得到了一组可以用统计方法分析的数字。下表展示了我们的数据集。

University	Typical A-level Offer	UCAS Tariff Points
University of Oxford	A*A*A	160
University of Cambridge	A*A*A	160
Imperial College London	A*AA	152
University College London (UCL)	A*AA	152
London School of Economics (LSE)	A*AA	152
University of Warwick	A*AA	152
University of Edinburgh	AAA	144
University of Manchester	A*AA	152
University of Leeds	AAB	136
University of Liverpool	ABB	128

These tariff points now form our raw data set for statistical analysis. Notice that several universities share the same point value; this grouping will be useful when we look at frequency and the mode later.

这些关税积分现在构成了我们用于统计分析的原始数据集。注意，有几所大学的积分值是相同的；这种分组在我们后面研究频率和众数时会很有用。

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3. Organising Data: Frequency Table | 整理数据：频率表

A frequency table helps us see how often each tariff point value appears. We list the distinct point values, make a tally of each occurrence and then count the tally marks to give the frequency. The table below organises our university offer data.

频率表可以让我们看清每个积分值出现了多少次。我们列出不同的积分值，用划记符号记录每次出现，然后数出划记的个数得到频数。下面的表格整理了我们的大学录取数据。

Tariff Points	Tally	Frequency
128	I	1
136	I	1
144	I	1
152	IIII	5
160	II	2

From the frequency table, we can immediately see that 152 points is the most common requirement, while the highest and lowest values appear less frequently. This summary will make it easy to build a bar chart and compute statistics.

从频率表中我们立刻可以看出，152分是最常见的录取要求，而最高分和最低分出现的次数较少。有了这个汇总表，我们就能轻松地绘制柱状图并计算统计量。

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4. Visualising Data: Bar Chart | 数据可视化：柱状图

A bar chart is a great way to visualise the distribution of entry requirements. On the horizontal axis we place the tariff points (128, 136, 144, 152, 160), and on the vertical axis we show the frequency. Each category gets a bar whose height equals its frequency. For our data, the bar for 152 would be the tallest (height 5), while the bars for 128, 136 and 144 would each have height 1. The bars for 160 would reach height 2. Drawing this chart helps us quickly compare how many universities demand each points level.

柱状图是可视化入学要求分布的好方法。我们在横轴上标出积分值（128、136、144、152、160），在纵轴上表示频数。每个类别对应一个柱子，其高度等于该类的频数。对于我们的数据，152 分的柱子会是最高的（高度 5），而 128、136 和 144 分的柱子高度为 1。160 分的柱子高度为 2。画出这个图可以帮助我们快速比较有多少所大学要求每个分数水平。

To construct the bar chart yourself, you would draw and label the axes, choose a suitable scale (for example, 1 cm per university on the vertical axis), and then draw bars of equal width for each point value. Remember to leave gaps between the bars, because the categories are distinct and not part of a continuous scale.

要自己画出柱状图，你需要画出坐标轴并标上标签，选择合适的比例（例如纵轴上每厘米代表 1 所大学），然后为每个分数值画出宽度相等的柱子。记住柱与柱之间要留空隙，因为这些类别是不连续的，不像连续的尺子刻度。

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5. Measure of Central Tendency: Mean | 集中趋势度量：平均数

The mean (often called the average) gives us a typical tariff point value for the whole group of universities. To find the mean, we add together all the tariff points and then divide by the total number of universities.

平均数（通常被称为平均值）可以告诉我们这组大学的一个典型入学积分值。要计算平均数，我们需要把所有大学的积分加起来，然后除以大学的总数。

The sum of all tariff points is: 160 + 160 + 152 + 152 + 152 + 152 + 144 + 152 + 136 + 128 = 1488. There are 10 universities, so we divide the total by 10.

所有积分值的总和是：160 + 160 + 152 + 152 + 152 + 152 + 144 + 152 + 136 + 128 = 1488。一共有 10 所大学，所以我们将总和除以 10。

Mean = 1488 ÷ 10 = 148.8

The mean UCAS tariff requirement for this group of universities is 148.8 points. This value sits slightly below the most common offer of 152, because the lower requirements from Leeds and Liverpool pull the mean downwards.

这组大学的平均 UCAS 积分要求是 148.8 分。这个值略低于最常见的 152 分，因为利兹大学和利物浦大学较低的要求拉低了平均数。

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6. Finding the Median | 找中位数

The median is the middle value when all data points are arranged in order from smallest to largest. It is another useful average that is not influenced by very high or very low extremes.

中位数是将所有数据点从小到大排列后位于中间位置的数值。这是另一种有用的平均数，它不受极高或极低极端值的影响。

We first sort the 10 tariff points: 128, 136, 144, 152, 152, 152, 152, 152, 160, 160. Since there is an even number of values (10), the median is the mean of the 5th and 6th values. The 5th value is 152 and the 6th value is also 152.

我们先将 10 个积分值排序：128、136、144、152、152、152、152、152、160、160。因为数值的个数是偶数（10 个），中位数是第 5 个和第 6 个数值的平均数。第 5 个数值是 152，第 6 个数值也是 152。

Median = (152 + 152) ÷ 2 = 152

The median offer of 152 points confirms that half the universities require 152 or less, and half require 152 or more. Here the median equals the most frequent value, which is a helpful coincidence.

中位数 152 分表明，有一半的大学要求 152 分或以下，另一半要求 152 分或以上。这里中位数正好等于最常见的值，这是一个有用的巧合。

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7. Identifying the Mode | 找众数

The mode is the data value that appears most often. It is especially useful for categorical or discrete data like university tariff points, because it shows the most typical requirement that a student may encounter.

众数是出现次数最多的数据值。对于像大学积分这种离散数据，众数尤其有用，因为它揭示了学生最可能遇到的典型录取要求。

Looking back at our frequency table, the tariff point 152 appears five times, more than any other value. Therefore, the mode is 152 points. This makes sense because five out of the ten universities in our list (Imperial, UCL, LSE, Warwick and Manchester) all ask for A*AA, which is a very common top offer.

回顾我们的频率表，152 分出现了五次，比任何其他值都多。因此，众数是 152 分。这很合理，因为我们列表中的十所大学里有五所（帝国理工、UCL、LSE、华威和曼彻斯特）都要求 A*AA，这是一个非常常见的高要求组合。

If two values tied for the highest frequency, the data set would be called ‘bimodal’. In our case, there is a clear single mode.

如果两个数值的最高频数相同，这个数据集就被称为“双众数”。在我们的例子中，有一个明确的单一众数。

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8. Measure of Spread: Range | 离散度量：范围

The range tells us how spread out the data are. It is calculated by subtracting the smallest value from the largest value. A large range indicates a wide variation in university requirements, while a small range would mean the offers are very similar.

范围告诉我们数据的离散程度。它通过用最大值减去最小值来计算。范围大表明大学的入学要求差异很大，而范围小则意味着录取条件非常相似。

Our smallest tariff point value is 128 (Liverpool) and the largest is 160 (Oxford and Cambridge).

我们数据集中的最小积分值是 128（利物浦大学），最大是 160（牛津大学和剑桥大学）。

Range = 160 – 128 = 32

The range of 32 points shows that there is a noticeable

Published by TutorHao | Year 7 统计 Revision Series | aleveler.com

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