📚 Summer Preparation and Transition Course for Year 7 Edexcel Statistics | Year 7 Edexcel 统计：暑期预习与衔接课程
Moving from primary to secondary school is a big step, and Year 7 Statistics will open your eyes to the exciting world of data. This summer preparation course is designed to introduce you to the key ideas you will meet in your Edexcel lessons – from collecting data and drawing charts to finding averages and understanding probability. By working through these topics, you will build confidence and be ready to handle data like a true mathematician from your very first week.
从小学升入中学是重要的一步，七年级统计课将为你打开数据世界的精彩大门。这份暑期预习与衔接课程专为帮助你提前了解 Edexcel 课程的核心概念而设计——从收集数据、绘制图表，到计算平均数和理解概率。通过梳理这些主题，你将逐步建立信心，在开学第一周就能像一位小小数学家那样轻松处理数据。
1. What is Statistics? | 什么是统计？
Statistics is the branch of mathematics that deals with collecting, organising, presenting, and interpreting data. When you ask questions like “What is the most popular fruit in our class?” or “How tall are Year 7 students?”, you are starting a statistical investigation. The process usually follows four stages: pose a question, gather information, display the data in charts or tables, and then make sense of the results.
统计学是数学的一个分支，研究如何收集、整理、展示和解读数据。当你提出“我们班最喜欢的水果是什么？”或“七年级学生有多高？”这样的问题时，就已经开启了一项统计调查。整个过程通常遵循四个阶段：提出问题、收集信息、用图表或表格展示数据，然后理解结果的含义。
In Year 7, you will learn how to turn everyday questions into statistical projects. You will discover that data is everywhere – in sports scores, weather records, and even in your favourite games. Being able to read and understand data helps you make better decisions and back up your opinions with evidence.
在七年级，你将学习如何把日常问题转变成统计项目。你会发现数据无处不在——体育比分、天气记录，甚至你最喜欢的游戏里都有。能够读懂并理解数据，有助于你做出更好的决定，并用证据支持自己的观点。
2. Types of Data: Qualitative and Quantitative | 数据类型：定性与定量
Before you start analysing, it is important to know what kind of data you are dealing with. Data can be qualitative or quantitative. Qualitative data describes qualities or categories – think of eye colour, favourite subject, or type of pet. You cannot do arithmetic with words, but you can count how many people fall into each category.
在开始分析之前，了解你处理的是哪种数据非常重要。数据可分为定性数据和定量数据。定性数据描述的是品质或类别——想想眼睛的颜色、最喜欢的科目或宠物种类。你不能对词语做算术运算，但可以计算每个类别中有多少人。
Quantitative data is numerical – it tells you how much or how many. Height, time, test scores, and number of siblings are all quantitative. Quantitative data can be discrete (counted, like number of books) or continuous (measured, like length or temperature). Recognising the type of data helps you choose the right chart and the best way to summarise it.
定量数据是数值型的——它告诉你多少或多高。身高、时间、考试分数和兄弟姐妹数量都是定量数据。定量数据又可分为离散数据（可数的，如书本数量）和连续数据（可测量的，如长度或温度）。识别数据类型能帮助你选择合适的图表和最佳的汇总方式。
3. Collecting Data – Surveys and Questionnaires | 收集数据：调查与问卷
A survey is a method of gathering information from a group of people. In Year 7, you will often design simple questionnaires. Good questions are clear, fair, and give you the exact data you need. For example, asking “How many hours do you spend on homework each week?” is better than a vague question like “Do you study a lot?” because it gives you numerical responses.
调查是从一组人中收集信息的方法。在七年级，你经常会设计简单的问卷。好的问题清晰、公正，并能提供你所需的准确数据。例如，问“你每周花多少小时做作业？”就比“你学习很多吗？”这样模糊的问题更好，因为前者可以得到数值型的回答。
It is also crucial to avoid leading or biased questions. A question like “Don’t you agree that maths is the best subject?” pushes people towards a particular answer. Instead, you could ask “What is your favourite subject?” and list several options. Collecting data fairly ensures your conclusions are trustworthy.
避免引导性或带有偏见的问题也至关重要。像“你难道不认为数学是最好的科目吗？”这样的问题会把人们推向某个特定答案。你可以改为问“你最喜欢的科目是什么？”并列出多个选项。公平地收集数据能确保你的结论值得信赖。
4. Tally Charts and Frequency Tables | 计数图与频率表
Once you have collected raw data, you need to organise it. A tally chart is a quick way to record counts. Each response is marked with a stroke, and every fifth stroke is drawn diagonally across the previous four to make a group of five – this makes counting much faster. The tally marks are then converted into numbers to create a frequency table.
一旦收集了原始数据，就需要对其进行整理。计数图是一种快速记录数量的方法。每出现一次回答就划一道线，每五道线组成一组（第五道斜线划过前四道），这样数数会快得多。然后将计数转换为数字，就形成了频率表。
A frequency table lists each category or value alongside the number of times it appears (the frequency). It turns messy data into an organised summary, ready for drawing graphs. For example, if you surveyed 30 students about their favourite colour, your frequency table might show Red: 8, Blue: 12, Green: 6, Other: 4. This gives you a clear picture before you even draw a chart.
频率表列出每个类别或数值及其出现的次数（频率）。它将杂乱的数据变成井井有条的汇总，为绘制图表做好准备。例如，如果你调查了 30 名学生最喜欢的颜色，频率表可能会显示红色：8，蓝色：12，绿色：6，其他：4。这样在绘图之前你就能一目了然。
5. Bar Charts and Pictograms | 条形图与象形图
Bar charts are probably the most common way to display categorical data. In a bar chart, each category gets its own bar, and the height (or length) of the bar shows the frequency. Bars must be of equal width and should not touch each other – the gaps emphasise that categories are separate. Always label the axes and give the chart a title.
条形图可能是展示分类数据最常用的方式。在条形图中，每个类别都有一个独立的条形，条形的高度（或长度）表示频率。所有条形的宽度必须相等，且条形之间不应接触——留出的间隔强调类别是彼此独立的。务必标注坐标轴并给图表加上标题。
Pictograms use small pictures or symbols to represent a certain number of items. A key explains what each symbol stands for – for example, one book icon equals 2 books read. Pictograms are visually appealing and easy to understand, but they are less precise than bar charts when data does not fit neatly into whole symbols. You will learn when each type of graph works best.
象形图使用小图片或符号来表示一定数量的物品。图例说明每个符号代表的数量——例如，一本书的图标代表读了 2 本书。象形图视觉吸引力强且易于理解，但当数据不能恰好用完整符号表示时，就不如条形图精确。你将学习每种图形在什么情况下最适用。
6. Pie Charts | 饼图
A pie chart shows how a whole is divided into parts. The circle represents all the data (100%), and each slice corresponds to a category’s proportion. To draw a pie chart, you need to calculate the angle for each slice using the formula: angle = (frequency ÷ total frequency) × 360°. This links your knowledge of angles and fractions to statistics.
饼图展示一个整体如何被划分成若干部分。整个圆代表所有数据（100%），每一块扇区对应一个类别的比例。要绘制饼图，你需要用公式计算每个扇形的角度：角度 =（频率 ÷ 总频率）× 360°。这把你对角度和分数的知识同统计联系了起来。
Pie charts are excellent for showing relative sizes, especially when you have only a few categories. However, they become messy with too many slices. In Year 7, you will practise drawing pie charts with a protractor and interpreting them – for instance, spotting that the largest slice represents the mode, or comparing two slices visually.
饼图非常适合展示相对大小，尤其是在类别不多的时候。但如果分类过多，图表会变得杂乱。在七年级，你将练习用量角器绘制饼图并解读它们——例如，发现最大的扇区代表众数，或者直观地比较两个扇区的大小。
7. Line Graphs | 折线图
Line graphs are used to display data that changes over time. You plot points for each time period and join them with straight lines. The horizontal axis usually shows time (days, months, years) and the vertical axis shows the variable being measured, such as temperature or height of a plant.
折线图用于展示随着时间变化的数据。你为每一个时间点标出数据点，然后用直线把它们连接起来。横轴通常表示时间（天、月、年），纵轴表示被测量的变量，比如温度或植物高度。
A key skill in Year 7 is reading values from a line graph and describing trends. You might say “the temperature increased steadily from January to July, then fell sharply.” Line graphs help you see patterns and make predictions. Always check the scale on both axes before reading off numbers – small mistakes can lead to wrong conclusions.
七年级的一项关键技能是从折线图中读取数值并描述趋势。你可能会说“温度从一月到七月稳步上升，然后急剧下降”。折线图帮助你发现规律并做出预测。在读取数值之前，务必检查两个坐标轴上的刻度——小小的疏忽可能导致错误的结论。
8. Averages: Mean, Median, Mode | 平均数：均值、中位数、众数
An average is a single value that summarises a set of numbers. The three main averages are the mode, median, and mean. The mode is the value that appears most often – it is the only average that works for qualitative data. The median is the middle value when the numbers are put in order. If there are two middle numbers, take the mean of those two.
平均数是一个能概括一组数据的单一数值。三种主要的平均数是众数、中位数和均值。众数是出现次数最多的数值——它是唯一能用于定性数据的平均数。中位数是将所有数值按顺序排列后处于中间位置的值。如果有两个中间的数，则取这两个数的均值。
The mean is what many people call “the average”. To find the mean, add up all the values and then divide by the number of values. In symbols: Mean = sum of data values ÷ number of values. For example, the mean of 4, 8, 6 is (4+8+6) ÷ 3 = 6. The mean uses every piece of data, so it can be affected by very high or low outliers.
均值就是许多人常说的“平均数”。要计算均值，先把所有数值相加，然后除以数值的个数。用符号表示：均值 = 数据值之和 ÷ 值的个数。例如，4、8、6 的均值是 (4+8+6) ÷ 3 = 6。均值用到了每一个数据，因此会受到极高或极低异常值的影响。
Knowing which average to use depends on the data and what you want to show. The median is often better when data is skewed because it is not pulled by outliers. In Year 7, you will practise calculating all three and choosing the most appropriate one for the situation.
知道选用哪种平均数取决于数据本身以及你想展示的内容。当数据分布偏斜时，中位数往往更好，因为它不会被异常值拉偏。在七年级，你将练习计算这三种平均数，并学会根据情况选择最合适的一种。
9. Range – Measuring Spread | 极差：衡量离散程度
The range tells you how spread out the data is. It is the difference between the largest and smallest values. A small range means the numbers are close together; a large range means they are more spread out. To calculate the range, simply subtract the minimum from the maximum.
极差告诉你数据的分散程度。它是最大值与最小值之间的差。极差小意味着数值比较集中；极差大意味着数值比较分散。要计算极差，只需用最大值减去最小值。
For example, if the test scores in one class are 12, 14, 15, 16, 19, the range is 19 – 12 = 7. The range is quick to compute, but it only uses two values and can be distorted by a single extreme outlier. Together with an average, the range gives a simple summary of both the centre and the spread of a dataset.
例如，如果某次测验的成绩为 12、14、15、16、19，那么极差就是 19 – 12 = 7。极差计算起来很简便，但它只用到两个值，很容易被单独一个极端异常值扭曲。将极差与平均数结合使用，就能简要概括数据集的中心和离散程度。
10. Introduction to Probability | 概率入门
Probability is the chance that something will happen. In Year 7, you start by using words to describe probability: impossible, unlikely, even chance, likely, certain. Later, you express probabilities as numbers between 0 (impossible) and 1 (certain), often as fractions. For example, when you toss a fair coin, the probability of getting heads is ½.
概率是指某件事情发生的可能性。在七年级，你首先会用词语描述概率：不可能、不太可能、对半机会、很可能、一定发生。之后，你会把概率表示为 0（不可能）到 1（一定发生）之间的数字，通常写成分数。例如，抛掷一枚均匀硬币，得到正面朝上的概率是 ½。
You will investigate simple experiments, such as rolling a dice or picking a card, and record outcomes. The probability of an event is calculated as: probability = number of successful outcomes ÷ total number of possible outcomes, provided all outcomes are equally likely. So, the probability of rolling an even number on a six-sided dice is 3/6, which simplifies to ½.
你将探究简单的实验，如掷骰子或抽卡片，并记录结果。在等可能的前提下，某事件的概率计算公式为：概率 = 成功结果的数量 ÷ 所有可能结果的总数。因此，掷一个六面骰子掷出偶数的概率是 3/6，约简后为 ½。
A common mistake is to confuse probability with real-life wishes – just because the probability of rain is low does not mean it will definitely stay dry. Understanding probability helps you assess risk and make informed predictions.
一个常见的错误是把概率和现实生活中的愿望混为一谈——降雨概率低并不代表天气一定会保持干燥。理解概率有助于你评估风险并做出有根据的预测。
11. Interpreting Statistical Diagrams | 解读统计图表
Drawing graphs is only half the story – you also need to read and criticise them. When you look at a bar chart, pie chart, or line graph, always check the title, axis labels, and scale. Ask yourself: what is this graph telling me? Can I spot any trends or surprising results?
绘制图表只是故事的一半——你还需要学会阅读和评判它们。当你查看条形图、饼图或折线图时，一定要检查标题、坐标轴标签和刻度。问一问自己：这张图在告诉我什么？我能发现什么趋势或令人惊讶的结果吗？
Be aware of misleading graphs. Sometimes axes do not start at zero, which can exaggerate small differences. A pictogram might use symbols of different sizes, giving a false impression. In Year 7, you will start to spot these tricks and explain why a graph might be biased or unclear. This critical thinking skill will serve you well beyond the classroom.
要警惕具有误导性的图表。有时候坐标轴不以零为起点，这会夸大细微的差异。象形图可能使用不同大小的符号，给人错误的印象。在七年级，你将开始识别这些“花招”，并解释为什么某张图可能有偏见或表达不清。这项批判性思维技能对你课堂内外的成长都大有裨益。
12. Summer Practice: Get Ready for Year 7 | 暑期练习：为七年级做好准备
The best way to prepare for Year 7 Statistics is to become a data detective over the summer. Try this mini-project: pick a question that interests you – for example, “What is the most common shoe size in my family?” or “How many pets do my friends have?” – and collect data from at least 15 people. Record your results in a tally chart and a frequency table.
为七年级统计课做准备的最好方法，就是在暑期当一回数据侦探。不妨试试这个小项目：选一个你感兴趣的问题——比如“我的家人最常见的鞋码是多少？”或“我的朋友养了多少只宠物？”——然后从至少 15 个人那里收集数据。把你的结果记录到计数图和频率表中。
Next, draw a suitable chart – a bar chart for shoe sizes or a pie chart if you want to show the proportion of people with 0, 1, or 2 pets. Calculate the mode and the range of your data, and challenge yourself to find the mean and median as well. Write two or three sentences explaining what your data tells you. You could even present your findings to your family!
接下来，绘制一张合适的图表——可以用条形图表示鞋码，或者如果想展示养 0 只、1 只或 2 只宠物的人数比例，就画一张饼图。计算数据的众数和极差，并挑战自己再求出均值和中位数。写两三句话解释你的数据告诉了你什么。你甚至可以向家人展示你的发现！
Also, spend a little time playing probability games: flip coins, roll dice, and keep a record of outcomes. Compare your experimental results with the theoretical probabilities. These hands-on activities will make the abstract ideas of statistics feel real and fun – and you will walk into your first Year 7 lesson ready to excel.
此外，花一点时间玩概率游戏：抛硬币、掷骰子，并记录结果。把你的实验结果同理论概率进行比较。这些动手活动会让抽象的统计概念变得真实而有趣——你将带着充分的准备走进第一节七年级统计课，迎接出色的表现。
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