📚 Cambridge Year 7 Statistics: Summer Bridging Course | 剑桥 Year 7 统计：暑期预习与衔接课程
Welcome to your summer bridging course designed to give you a head start in Year 7 Cambridge Statistics. This guide introduces the essential ideas and vocabulary you will meet, from types of data and how to collect it, to drawing charts and finding averages. By working through these sections before the new term, you will build confidence and be ready to explore data with curiosity and a clear structure.
欢迎来到专为 Year 7 剑桥统计设计的暑期衔接课程，帮助你提前起步。本指南将介绍你将遇到的核心概念与术语：从数据的类型与收集方法，到绘制图表与计算平均数。在开学前通读这些小节，你会建立信心，带着好奇和清晰的框架去探索数据。
1. Welcome to Statistics | 欢迎来到统计学
Statistics is the science of collecting, organising, presenting, analysing and interpreting data. Every time you look at a weather forecast, check sports scores or read a poll, you are seeing statistics in action. In Year 7, you will learn how to ask sensible questions, gather information and turn raw numbers into clear pictures and summaries.
统计学是收集、整理、呈现、分析和解释数据的科学。每当你看天气预报、查看体育比分或阅读民调时，你都在接触统计学。在 Year 7，你将学习如何提出合理的问题、收集信息，并将原始数字转化为清晰的图表和摘要。
This bridging course will walk you through the key topics step by step. You will meet new words like ‘frequency’, ‘average’ and ‘range’, and you will practise using them to describe real situations. Keep a notebook handy to jot down ideas and try the little challenges along the way.
本衔接课程将带你逐步走过各个关键主题。你会遇到诸如 “频数”、“平均数”、“极差” 等新词汇，并练习用它们描述真实情景。准备一个笔记本，随时记录想法，并尝试课程中的小挑战。
2. Why Statistics Matters | 为什么统计学很重要
Statistics helps us make sense of the world by turning information into evidence. Doctors use statistics to understand the effectiveness of treatments. Shop managers look at sales data to decide which items to restock. Even video game designers study player data to make games more fun.
统计学通过将信息转化为证据，帮助我们理解世界。医生用统计了解治疗效果；商店经理查看销售数据决定补货商品；甚至电子游戏设计师也会研究玩家数据让游戏更有趣。
In your own life, you already use statistical thinking when you compare prices, check the chance of rain or look at your class test scores. Understanding basic statistics gives you the power to ask better questions and not be tricked by misleading graphs or claims.
在你自己的生活中，当比较价格、查看降雨概率或看班级测验成绩时，你已经在使用统计思维。理解基础统计能让你提出更好的问题，不被误导的图表或说法欺骗。
3. Types of Data | 数据的类型
Data can be classified into two broad types: categorical (qualitative) and numerical (quantitative). Categorical data describe qualities or groups. Examples are favourite colour, type of pet or eye colour. Numerical data are numbers that can be measured or counted.
数据可以分为两大类：类别数据（定性数据）和数值数据（定量数据）。类别数据描述品质或组别，例如最喜欢的颜色、宠物类型或眼睛颜色。数值数据是可以测量或计数的数字。
Numerical data can be further split into discrete and continuous. Discrete data are counted and can only take certain values – usually whole numbers, like the number of books in a bag or shoe size. Continuous data are measured and can take any value within a range, such as height, mass or time taken to run 100 metres.
数值数据可进一步分为离散数据和连续数据。离散数据是计数得到的，只能取特定值，通常为整数，如书包里的书本数或鞋码。连续数据是测量得到的，在一个范围内可取任意值，如身高、质量或跑 100 米的时间。
Being able to tell the difference helps you choose the right chart and the right average later. Ask yourself: ‘Am I counting or measuring? Am I describing a quality or a quantity?’
能够区分数据的类型有助于你日后选择正确的图表和平均数。问自己：“我是在计数还是测量？我是在描述一种特质还是一个数量？”
4. Collecting Data | 收集数据
Before we can analyse anything, we need to collect reliable data. Common methods include surveys, questionnaires, experiments and direct observations. When you design a survey, make sure the questions are clear and fair. For example, instead of asking ‘Don’t you think chips are delicious?’, ask ‘How much do you like chips?’ and give options like ‘Not at all, A little, Quite a lot, Very much’.
在分析任何事物之前，我们需要收集可靠的数据。常用的方法有调查、问卷、实验和直接观察。设计调查时，要确保问题清晰且公正。例如，与其问“你不觉得薯条很好吃吗？”，不如问“你有多喜欢薯条？”并提供“一点也不、一点点、比较多、非常多”等选项。
When recording data, we often use tally marks. Every item gets one mark: | for 1, || for 2, ||| for 3, |||| for 4, and the fifth mark goes diagonally across the four. This groups data into fives, making it much quicker to count later.
记录数据时，我们常使用划记符号。每个项目划一道：| 表示 1，|| 表示 2，||| 表示 3，|||| 表示 4，第五道对角划过四道。这样每五个一组，方便以后快速计数。
5. Organising Data with Tally Charts | 用划记表整理数据
A tally chart is a simple table that shows categories, tally marks and frequencies. It keeps your data organised while you collect it. Each group of five tallies looks like a little gate, which is easy to read.
划记表是一个简单的表格，展示类别、划记符号和频数。它在收集数据的同时帮你保持条理。每五个划记组成一个像小门一样的符号，非常易读。
Below is an example tally chart for favourite fruits in a class. Watch how the tallies turn into frequencies.
下面是一个班级最喜欢水果的划记表示例。注意看划记如何转化为频数。
| Favourite fruit | Tally | Frequency |
|---|---|---|
| Apple | |||| | 4 |
| Banana | |||| || | 7 |
| Orange | |||| ||| | 8 |
| Grapes | ||| | 3 |
Once the tally chart is complete, you can use the frequencies to draw graphs or find the mode. Always double‑check your counts – a missing tally can change your results.
划记表完成后，你可以用频数绘制图表或寻找众数。务必反复核对计数——漏掉一划就可能改变结果。
6. Frequency Tables | 频数表
A frequency table is like a clean, final version of a tally chart. It lists the categories or values and tells you how many times each one occurs. Tally marks are removed, leaving only numbers.
频数表就像划记表的整洁定型版本。它列出各个类别或数值，并告诉你每个出现的次数。划记符号被去掉，只保留数字。
Frequency tables can also be used for grouped numerical data. For example, if you record the times (in seconds) it takes students to solve a puzzle, you might group them: 0–9 s, 10–19 s, 20–29 s and so on. The table then shows how many students fall into each group.
频数表也可用于分组数值数据。例如，记录学生解谜题的用时（秒），你可以分组：0–9 秒、10–19 秒、20–29 秒等。表格随后显示每组有多少学生。
Reading a frequency table correctly is a skill that will help you answer questions like ‘Which category is the most popular?’ and ‘How many more in one group than another?’. Always look at the title and column headings first.
正确阅读频数表是一项技能，能帮你回答诸如“哪个类别最受欢迎？”和“一组比另一组多多少？”的问题。务必先看表格标题和列名称。
7. Bar Charts and Pictograms | 条形图与象形图
Bar charts (also called bar graphs) represent frequencies using rectangular bars. The bars must have equal width and be separated by gaps to show the categories are distinct. The height of each bar matches the frequency. Always label your axes and give the chart a title.
条形图（也称条形统计图）用长条表示频数。各条的宽度必须相等，且条与条之间要有空隙，以表明类别是互相独立的。每一条的高度与频数匹配。务必给坐标轴标上名称并给图表加上标题。
Pictograms use small pictures or symbols to represent data. Each picture stands for a certain number of items. For instance, one tennis ball icon might represent 2 real tennis balls. A pictogram key is essential so that anyone reading the graph knows what each symbol means. When a fraction of a picture is shown, it represents a part of the value.
象形图用小图片或符号表示数据。每张图代表一定数量的项目。例如，一个网球图标可能代表 2 个真实的网球。象形图的图例必不可少，这样读图者才能知道每个符号代表什么。当出现部分图片时，它代表数值的一部分。
Both types of graph turn numbers into a visual story, making it easier to spot the largest and smallest categories at a glance.
这两类图表都将数字变成了视觉故事，让人一眼就能看出最大和最小的类别。
8. Pie Charts | 饼图
A pie chart is a circle divided into sectors, each representing a category. The size of the sector shows the proportion of the whole. To draw a pie chart accurately, you must calculate the angle for each category using the formula:
饼图是一个被划分为若干个扇形的圆，每个扇形代表一个类别。扇形的大小表示该类别占总体的比例。要准确画出饼图，必须用公式计算每个类别的角度：
Angle = (Frequency ÷ Total frequency) × 360°
角度 = (频数 ÷ 总频数) × 360°
For example, if 10 out of 40 students chose ‘cycling’ as their favourite activity, the angle would be (10 ÷ 40) × 360° = 90°, which is a right angle. Pie charts are excellent for showing relative shares, but they are less useful when there are many small categories.
例如，40 名学生中有 10 人选择“骑自行车”作为最喜爱的活动，那么角度为 (10 ÷ 40) × 360° = 90°，即一个直角。饼图非常擅长展示相对份额，但当有很多小类别时用处就差一些。
9. The Mean (Average) | 均值（平均数）
The mean is what most people call the ‘average’. It is found by adding up all the values and then dividing by the number of values. The mean represents a central or typical value of the data set.
均值就是大多数人所说的“平均数”。其计算方法是：将所有数值相加，再除以数值的个数。均值代表数据集的中心或典型值。
Mean = (x₁ + x₂ + … + xₙ) ÷ n
均值 = (x₁ + x₂ + … + xₙ) ÷ n
Imagine you scored 6, 8, 7, 9 and 10 in five quizzes. The sum is 40 and there are 5 scores, so the mean is 40 ÷ 5 = 8. The mean does not have to be one of the actual data values – it is a summary. It can be affected by extremely large or small values, called outliers.
假设你在五次小测验中分别得到 6、8、7、9、10 分。总和是 40，有 5 个分数，因此均值为 40 ÷ 5 = 8。均值不一定是实际数据中的某一个值——它是一个概括值。均值会受到极大或极小值（即离群值）的影响。
10. Median and Mode | 中位数与众数
The median is the middle value when the data are put in order from smallest to largest. If there is an odd number of values, the median is the exact middle one. If there is an even number, you take the mean of the two middle numbers.
中位数是把数据从小到大排列后位于中间的值。如果数据个数是奇数，中位数就是正中间的那个；如果是偶数，则取中间两个数的均值。
For the quiz scores 3, 5, 7, 8, 12, the median is 7. For the set 3, 5, 7, 8, the median is (5 + 7) ÷ 2 = 6. The median is useful because it is not affected by outliers. A family’s house price data often uses the median rather than the mean for that reason.
对于测验分数 3, 5, 7, 8, 12，中位数是 7。对于集合 3, 5, 7, 8，中位数是 (5 + 7) ÷ 2 = 6。中位数很有用，因为它不受离群值影响。因此，家庭房价数据常用中位数而非均值。
The mode (or modal value) is the value that appears most often. A set of data can have one mode, more than one mode (bimodal or multimodal) or no mode at all if all values are equally frequent. The mode is the only average that can be used with categorical data.
众数（或众数值）是出现次数最多的值。一组数据可以有一个众数、多个众数（双众数或多众数），或者如果没有重复值则可没有众数。众数是唯一可以用于类别数据的平均数。
11. The Range | 极差
The range measures how spread out the data are. It is the difference between the largest and the smallest values. A large range tells you the data are very spread; a small range suggests the values are quite close together.
极差衡量数据的离散程度。它是最大值与最小值之间的差。极差很大说明数据非常分散；极差很小则说明数值比较接近。
Range = Maximum value – Minimum value
极差 = 最大值 – 最小值
If the highest daily temperature in a week was 22 °C and the lowest was 14 °C, the range is 8 °C. Always state the unit with the range when it has one. The range is a quick measure of variability, but it only uses two numbers and ignores everything else.
如果一周最高日温为 22 °C，最低为 14 °C，则极差为 8 °C。有单位时要注明单位。极差是度量变异性的快速方法，但它只使用了两个数字，忽略了其他所有信息。
12. Introduction to Probability | 概率入门
Probability is the branch of maths concerned with how likely events are to happen. It links closely with statistics because we often use data to estimate probabilities. Probability is measured on a scale from 0 (impossible) to 1 (certain).
概率是数学中关注事件发生可能性大小的分支。它与统计紧密相连，因为我们常利用数据来估计概率。概率的度量范围从 0（不可能）到 1（一定发生）。
Probability = Number of favourable outcomes ÷ Total number of possible outcomes
概率 = 有利结果的数量 ÷ 所有可能结果的总数
When you toss a fair coin, there are two equally likely outcomes: heads or tails. The probability of getting heads is 1 ÷ 2 = ½. You can also write probabilities as decimals or percentages. The terms ‘even chance’, ‘likely’, ‘unlikely’ and ‘certain’ are useful for describing probabilities in words.
抛一枚均匀硬币时，有两种等可能的结果：正面或反面。得到正面的概率是 1 ÷ 2 = ½。你也可以用小数或百分数表示概率。“等可能”、“很可能”、“不太可能”和“一定”这些词用于口头描述概率。
Remember, probability does not tell you exactly what will happen on a single trial – it tells you what to expect in the long run. That is why collecting plenty of data is so important.
记住，概率并不会告诉你单次试验中确切会发生什么——它告诉你的是长期趋势中可以期望的结果。这就是为什么收集大量数据如此重要。
Published by TutorHao | Statistics Revision Series | aleveler.com
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