📚 Year 7 AQA Statistics: Summer Preparation and Bridging Course | Year 7 AQA 统计：暑期预习与衔接课程
Welcome to your summer bridging course for Year 7 AQA Statistics! This article will introduce the key ideas you will meet in September – from collecting data to drawing charts and calculating averages. We have designed it to give you a head start, with clear explanations, examples, and activities you can try at home. You do not need any previous knowledge of statistics; just bring your curiosity and a willingness to explore numbers in the world around you.
欢迎来到 Year 7 AQA 统计的暑期衔接课程！这篇文章将为你介绍九月份将会接触到的关键概念——从收集数据到绘制图表，再到计算平均数。我们为你提供清晰的讲解、实例以及可以在家尝试的活动，帮助你领先一步。你不需要任何统计基础，只需带着好奇心和探索身边数字的热情就可以了。
Statistics is the science of learning from data. In Year 7, you will discover how to ask good questions, organise information, and present it so that others can understand it easily. This bridging resource covers each topic step by step, so that by the end you will feel confident and ready to start the new school year.
统计学是从数据中学习的科学。在 Year 7，你将学会如何提出好问题、整理信息并用他人容易理解的方式展示出来。本衔接材料将逐步覆盖每个主题，学完之后你会感到自信满满，为新的学年做好准备。
1. What is Statistics? | 什么是统计学？
Statistics is the branch of mathematics that deals with collecting, organising, analysing, and interpreting data. Data are simply pieces of information. For example, the heights of pupils in your class, the colours of cars in a car park, or the results of a survey about favourite sports are all data. In statistics, we use numbers and graphs to tell a story about what the data shows.
统计学是数学的一个分支，涉及收集、整理、分析和解读数据。数据就是一些信息片段。例如，你们班同学的身高、停车场里汽车的颜色、或者一项关于最喜爱运动的调查结果，都是数据。在统计中，我们使用数字和图表来讲述数据所显示的故事。
You will encounter statistics everywhere in daily life: news reports use percentages and charts, school newsletters show survey results, and weather forecasts use probability. Learning the basics in Year 7 will help you think critically about the information you see and make better decisions.
你在日常生活中会处处遇见统计：新闻报道使用百分数和图表，学校通告展示调查结果，天气预报则运用概率。在 Year 7 学习基础知识可以帮助你批判性地看待你看到的信息，并做出更好的决定。
2. Types of Data | 数据的类型
Before we can work with data, we need to understand what kind of data we are dealing with. The two main categories are qualitative (or categorical) data and quantitative data. Qualitative data is non‑numerical; it describes qualities or groups, such as eye colour, favourite subject, or type of pet. Quantitative data is numerical and comes in two types: discrete and continuous.
在我们处理数据之前，需要先了解我们处理的是哪种类型的数据。两大类数据是定性（或称分类）数据和定量数据。定性数据是非数值的，它描述特征或分组，比如眼睛颜色、最喜爱的科目或宠物类型。定量数据是数值型的，又分为两种：离散数据和连续数据。
Discrete data can only take certain specific values, usually whole numbers that come from counting. Examples include the number of siblings you have, the number of books in a bag, or the score on a dice. Continuous data can take any value within a range and is usually measured, not counted. Examples include height, time, mass, and temperature. The table below summarises these types:
离散数据只能取某些特定的值，通常是由计数得出的整数。例如，你的兄弟姐妹数量、书包里书的数量或骰子的点数。连续数据可以在一个范围内取任意数值，并且通常是通过测量而非计数得到的。例如，身高、时间、质量和温度。下表总结了这些类型：
| Type | Description | Examples |
|---|---|---|
| Qualitative (Categorical) | Non‑numerical, sorted into categories | Hair colour, favourite food |
| Quantitative – Discrete | Numerical, takes certain values (counts) | Number of pets, shoe size |
| Quantitative – Continuous | Numerical, can take any value in a range (measurements) | Height, time taken for a race |
Recognising the data type is important because it affects how you organise the data and which charts or calculations make sense. For instance, you cannot find the mean of favourite colours, but you can find the mode.
识别数据类型很重要，因为它会影响你如何整理数据，以及哪些图表或计算是合理的。例如，你无法计算最喜爱颜色的平均数，但你可以找出众数。
3. Collecting Data | 收集数据
Data can be collected in different ways. Primary data is information you collect yourself directly, for example by conducting a survey, carrying out an experiment, or taking measurements. Secondary data is information someone else has already collected, such as data from a website, a book, or a government report. In Year 7, you will often design simple questionnaires to gather primary data.
数据可以通过不同方式收集。原始数据是你自己直接收集的信息，例如通过问卷调查、实验或测量。二手数据是别人已经收集好的信息，比如来自网站、书籍或政府报告的数据。在 Year 7，你经常会设计简单的问卷来收集原始数据。
A good survey question should be clear and unbiased. For example, asking “What is your favourite sport?” is better than asking “Don’t you agree football is the best sport?” because the second question leads the person towards a particular answer. You will also learn to use tally marks ( /, //, ///, ////, and a diagonal line for five) to record data efficiently when counting.
一个好的调查问题应该是清晰且无偏见的。例如，问“你最喜爱的运动是什么？”就比问“你难道不认为足球是最好的运动吗？”更好，因为第二个问题会引导回答者偏向某个特定答案。你还会学习使用计数符号（一、二、三、四、五用 “正” 或画斜线）来高效记录数据。
Here is an example of collecting data on favourite fruits using a tally chart:
下面是一个用计数表收集最喜爱水果数据的例子：
| Fruit | Tally | Frequency |
|---|---|---|
| Apple | //// | 4 |
| Banana | //// // | 7 |
| Orange | /// | 3 |
4. Organising Data in Tables | 在表格中整理数据
Once you have collected your data, you need to organise it so that you can spot patterns. A frequency table lists each category or number alongside how many times it occurs (its frequency). For larger sets of continuous data, you might group the values into intervals, creating a grouped frequency table. For instance, heights might be grouped into “120 cm – 129 cm”, “130 cm – 139 cm”, and so on.
收集好数据之后，你需要把它整理好，这样才能发现模式。频率表列出每个类别或每个数值，以及它出现的次数（频率）。对于较大的连续数据集，你可能需要将数值分组，形成分组频率表。例如，身高可以分成“120 cm – 129 cm”、“130 cm – 139 cm”等区间。
A well‑structured table should have clear headings and appropriate intervals. Make sure every data value can fall into one and only one group. For discrete data with many possible values, you might also group them, but be careful not to lose too much detail.
一个结构良好的表格应该有清晰的标题和恰当的分组区间。要确保每一个数据值都能归入并且只归入一个组。对于有多种可能取值的离散数据，你也可以进行分组，但要小心不要丢失太多细节。
5. Presenting Data with Charts | 用图表展示数据
Charts and graphs make it easier to see patterns and communicate findings. In Year 7 you will draw and interpret bar charts, pictograms, and pie charts. A bar chart uses bars of equal width to represent frequencies; the height of each bar shows how many. Bar charts are ideal for categorical or discrete data. Always label your axes and provide a title.
图表使人们更容易发现规律并传达结果。在 Year 7，你将绘制并解读条形图、象形图和饼图。条形图用等宽的条形来表示频率，每个条形的高度就代表数量。条形图非常适合分类数据或离散数据。绘制时务必标注坐标轴并给出标题。
A pictogram uses pictures or symbols to represent data. For example, one picture of a book might stand for 5 books read. The key tells the reader what each symbol represents. A pie chart is a circle divided into sectors, where each sector’s angle is proportional to the frequency. To draw a pie chart, you calculate the angle for each category using the formula: angle = (frequency ÷ total frequency) × 360°.
象形图用图片或符号来表示数据。例如，一本书的图标可以代表读了 5 本书。图例会告诉读者每个符号的含义。饼图是一个被划分成扇形的圆，每个扇形的角度与频率成比例。要绘制饼图，你需要用公式计算每个类别的角度：角度 = (频率 ÷ 总频率) × 360°。
When constructing charts, use a ruler and pencil. Choose a suitable scale for bar charts so that the bars fit neatly on the grid. For a pictogram, draw the symbols carefully and include half or quarter symbols if needed, showing them clearly in the key.
绘制图表时，应使用直尺和铅笔。为条形图选择合适的刻度，使条形整齐地排列在网格上。对于象形图，应仔细绘制符号，并在需要时使用半个或四分之一个符号，并在图例中清晰标示。
6. Averages: Mean, Median and Mode | 平均数：平均数、中位数和众数
An average is a single value that summarises a set of numbers. There are three types you will use in Year 7: the mean, the median, and the mode. The mean is calculated by adding up all the values and dividing by the number of values. We write this as:
平均数是用来概括一组数据的单一数值。在 Year 7 你将学习三种平均数：平均数（均值）、中位数和众数。平均数的计算方法是将所有数值相加，再除以数值的个数。我们可以这样表示：
Mean = (x₁ + x₂ + … + xₙ) ÷ n
The median is the middle value when the data is arranged in order. If there is an odd number of values, the median is the exact middle one. If there is an even number, the median is the mean of the two middle numbers. The mode is the value that appears most often. A set can have one mode, more than one mode (bimodal), or no mode at all.
中位数是将数据按顺序排列后最中间的那个值。如果数据个数为奇数，中位数就是正中间的那个数；如果为偶数，中位数则是中间两个数的平均数。众数是出现次数最多的那个值。一组数据可以有一个众数、多个众数（双众数），或者根本没有众数。
The following table summarises how to find each average for the data set: 3, 5, 5, 7, 10.
下表总结了如何为数据集 3, 5, 5, 7, 10 找出每种平均数：
| Average | Method | Result |
|---|---|---|
| Mean | (3+5+5+7+10) ÷ 5 | 6 |
| Median | Ordered: 3, 5, 5, 7, 10 → middle is the 3rd value | 5 |
| Mode | Most frequent value | 5 |
Choosing the most appropriate average depends on the data and what you want to show. The mean is affected by extremely high or low values, while the median is not. The mode is useful for non‑numerical data.
选择最合适的平均数取决于数据本身以及你想说明什么问题。平均数容易受到极高或极低值的影响，而中位数则不会。众数对非数值数据也很实用。
7. The Range | 极差
The range is a simple measure of how spread out the data is. To calculate the range, subtract the smallest value from the largest value:
极差是衡量数据分散程度的一种简单方法。要计算极差，用最大值减去最小值：
Range = Maximum value − Minimum value
For example, if the test scores are 12, 15, 18, 9, and 14, the range is 18 − 9 = 9. A larger range tells you the data is more spread out; a smaller range suggests the values are closer together. In Year 7, you will often compare sets of data by looking at both an average and the range.
例如，如果测试分数为 12, 15, 18, 9 和 14，那么极差就是 18 − 9 = 9。较大的极差说明数据比较分散；较小的极差则说明数值比较集中。在 Year 7，你经常会通过同时观察平均数和极差来比较不同的数据集。
8. Introduction to Probability | 概率入门
Probability is a measure of how likely something is to happen. It is expressed as a number between 0 and 1, with 0 meaning impossible and 1 meaning certain. You can also use words such as “unlikely”, “even chance”, “likely”, or “certain”. Probability often links with statistics when we use data from experiments or surveys to estimate chances.
概率是衡量某件事发生可能性大小的指标，用一个介于 0 到 1 之间的数字来表示，0 代表不可能，1 代表一定发生。你也可以使用诸如 “不太可能”、”一半对一半”、”很可能” 或 “一定” 这样的词语。当我们利用实验或调查数据来估计机会时，概率常常与统计联系在一起。
One way to think about probability is as a fraction: probability = (number of favourable outcomes) ÷ (total number of possible outcomes). For a fair six‑sided dice, the probability of rolling a 3 is ⅙. The probability of rolling an even number is 3/6, which simplifies to ½.
思考概率的一种方法是用分数表示：概率 = (有利结果的数量) ÷ (所有可能结果的总数)。对于一个均匀的六面骰子，掷出 3 的概率是 ⅙；掷出偶数的概率是 3/6，化简后为 ½。
The probability scale can be illustrated as:
概率尺度可以表示为：
0 (impossible) ― ¼ (unlikely) ― ½ (even chance) ― ¾ (likely) ― 1 (certain)
In Year 7, you will carry out simple probability experiments, such as tossing a coin or rolling a dice, and compare what you expect to happen with what actually occurs. This helps you understand that probability is about long‑term patterns, even if short‑term results can vary.
在 Year 7，你会进行一些简单的概率实验，比如抛硬币或掷骰子，并将你的预期与实际发生的情况进行比较。这可以帮助你理解，概率描述的是长期规律，即便短期结果可能会有变化。
9. Summer Practice Activities | 暑期练习活动
To make a strong start in September, try these hands‑on activities during the summer break. They are designed to be fun and to give you real experience in collecting and using data.
为了在九月份有一个好的开始，暑假期间不妨试试这些动手活动。它们设计得既有趣又能让你在收集和使用数据方面获得真实体验。
Activity 1: Family Transport Survey. Ask 10 family members or friends how they usually travel to work or school (walk, bus, car, bicycle, etc.). Record your results in a tally chart, then draw a bar chart. Find the mode – which method is most common?
活动一：家庭交通调查。询问 10 位家人或朋友，他们通常如何上班或上学（步行、公交、汽车、自行车等）。在计数表中记录结果，然后画一个条形图。找出众数——哪种出行方式最常见？
Activity 2: Daily Temperature. Record the temperature at the same time each day for one week. Calculate the mean temperature for the week and the range between the warmest and coolest days. Plot the temperatures on a simple line graph to see how they change.
活动二：每日温度。连续一周每天在同一时间记录温度。计算这一周的平均温度和最热与最冷天之间的极差。将温度画在简单的折线图上，观察它们如何变化。
Activity 3: Dice Probability. Roll two dice 30 times and add the scores each time. Keep a tally of the totals. Before you start, predict which total you think will appear most often. After the experiment, compare your prediction with the actual mode and discuss why 7 is more likely than 2 or 12.
活动三：骰子概率。每次掷两个骰子，将点数相加，共掷 30 次。用计数法记录每次的总和。在开始之前，预测一下你认为哪个总和会出现得最频繁。实验结束后，将预测与实际众数进行比较，并讨论为什么总和为 7 比 2 或 12 更容易出现。
10. Bridging Tips for Year 7 Statistics | Year 7 统计衔接技巧
Stepping into Year 7 statistics can feel like a big jump, but a few simple habits will make you feel at home. First, always ask questions when you see charts or data in the real world. What does the chart show? Is the scale fair? Could someone be trying to mislead you? This critical thinking will strengthen your classroom skills.
进入 Year 7 统计学习可能感觉像一个大跨越，但一些简单的好习惯会让你感到轻松自如。首先，当你在现实生活中看到图表或数据时，时刻问自己问题。这个图表展示了什么？刻度是否公正？是否有人想误导你？这种批判性思维会增强你的课堂能力。
Brush up on your basic arithmetic over the summer – adding, subtracting, multiplying, and dividing – because you will need these to calculate averages and totals. Practice mental maths and, when possible, work with small sets of numbers to find the mean and range quickly. Also, get comfortable using a ruler and protractor for drawing bar charts and pie charts.
在暑假期间复习基本的算术运算——加减乘除——因为你在计算平均数和总数时需要这些。练习心算，并尽可能地用小数据集快速求平均数和极差。同时，要熟练使用直尺和量角器来绘制条形图和饼图。
Finally, explore the statistics section of any recommended online resources or revision sites. Watching short videos on bar charts, averages, or probability can introduce you to the vocabulary and concepts in a low‑pressure way. Just 10–15 minutes a few times a week can build your confidence before September.
最后，可以浏览一些推荐的在线学习资源或复习网站上关于统计的部分。观看有关条形图、平均数或概率的短视频，能够在轻松的氛围中向你介绍相关词汇和概念。每周只需花 10 到 15 分钟，就能在九月开学前建立信心。
11. Common Mistakes to Avoid | 需要避免的常见错误
Even simple statistics
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