📚 Year 7 CAIE Statistics: Summer Prep and Bridging Course | 七年级 CAIE 统计：暑期预习与衔接课程
Welcome to the exciting world of statistics! This summer prep course is designed to give you a head start in Year 7 CAIE Statistics. You will explore how to collect, display and interpret data, and discover patterns that help us understand the world around us. No prior knowledge is needed — just bring your curiosity and a willingness to work with numbers and real-life situations.
欢迎来到令人兴奋的统计世界！本暑期预习课程旨在帮助你在七年级 CAIE 统计学习中抢占先机。你将学习如何收集、展示和解读数据，并发现那些帮助我们理解周边世界的规律。你不需要具备任何预备知识——只需带上好奇心和运用数字处理实际问题的意愿。
1. What is Statistics? | 什么是统计？
Statistics is the science of collecting, organising, analysing and interpreting data. Data simply means facts and figures, such as the heights of students in your class, the number of goals your team scored last season, or daily temperatures recorded over a week.
统计是收集、组织、分析和解读数据的科学。数据就是指事实和数字，例如班上同学的身高、你的球队上赛季的进球数，或者一周内记录的每日气温。
When you look at data, you can spot trends, compare groups and make predictions. Statistics turns raw numbers into meaningful stories that help us make sensible decisions.
当你观察数据时，可以发现趋势、比较不同群体并做出预测。统计将原始数字转化为有意义的故事，帮助我们做出明智的决定。
2. Collecting Data | 收集数据
Data can be collected in many ways: through surveys, experiments, observations or by using existing records. For example, you might design a short questionnaire to ask classmates about their favourite sport.
数据可以通过多种方式收集：调查、实验、观察或使用已有的记录。例如，你可以设计一份简短的问卷，询问同学们最喜欢的运动。
When you gather data yourself, it is called primary data. If you use data that someone else has already collected — like information from a website or a newspaper — it is called secondary data. Both types are useful, but you should always check if your source is reliable.
当你自己收集数据时，这叫做一手数据。如果你使用别人已经收集好的数据——比如来自网站或报纸的信息——则称为二手数据。两种类型都有用，但你始终要检查来源是否可靠。
3. Types of Data | 数据类型
Data can be qualitative or quantitative. Qualitative data describes qualities or categories, like eye colour, favourite food or types of pet. It often answers ‘what kind’ questions.
数据可以是定性或定量的。定性数据描述性质或类别，比如眼睛的颜色、喜欢的食物或宠物的种类，通常回答“哪种”的问题。
Quantitative data deals with numbers. It can be discrete — countable, like the number of siblings you have — or continuous — measurable, like your height or the time it takes to run 100 metres.
定量数据涉及数字。它可以是离散的——可数的，比如你有多少个兄弟姐妹——或者连续的——可测量的，比如你的身高或跑100米所用的时间。
| Data Type | Example |
| Qualitative | Hair colour: black, brown, blonde |
| Discrete quantitative | Number of books read in a month: 3, 5, 7 |
| Continuous quantitative | Mass of a pumpkin: 2.35 kg |
Knowing the type of data helps you choose the right way to display and analyse it.
了解数据类型有助于你选择正确的方式来展示和分析它。
4. Organising Data: Frequency Tables | 组织数据：频数表
A frequency table is one of the simplest ways to organise data. It lists each value along with how many times it appears. Tally marks (||||) are often used to count easily before writing the frequency.
频数表是组织数据最简单的方法之一。它列出每个值以及该值出现的次数。在写下频数之前，人们常用划线记数（||||）来方便计数。
Example: Shoe sizes of 12 students: 3, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 4. The frequency table would look like this:
示例：12名学生的鞋码：3, 4, 3, 5, 4, 3, 5, 4, 3, 5, 4, 4。频数表如下：
| Shoe size | Tally | Frequency |
| 3 | |||| | 4 |
| 4 | |||| | 5 |
| 5 | ||| | 3 |
Having a frequency table makes it much easier to draw charts and find averages later.
有了频数表，后续绘制图表和计算平均数会容易得多。
5. Pictograms and Bar Charts | 象形图和条形图
A pictogram uses symbols or pictures to represent data. Each picture stands for a certain number of items. For instance, one star might represent 2 students who chose reading as a hobby. Pictograms are visually appealing and easy to read.
象形图使用符号或图片来展示数据。每张图片代表一定数量的项目。例如，一颗星星可以代表两名选择阅读作为爱好的学生。象形图生动好看，容易阅读。
A bar chart uses rectangular bars to show frequencies. The height of each bar corresponds to the frequency. Bars must have equal width and be separated by gaps. Always label the axes and give the chart a title.
条形图使用矩形条来显示频数。每个条形的高度对应频数。条形宽度必须相等，条形之间留有空隙。永远要标记坐标轴并给图表加上标题。
In Year 7 you will learn to draw both vertical and horizontal bar charts, and also how to choose a suitable scale for the frequency axis.
在七年级你将学习绘制垂直和水平条形图，以及如何为频数轴选择合适的刻度。
6. Line Graphs and Pie Charts | 折线图和饼图
A line graph is ideal for showing how data changes over time. You plot points and join them with straight lines. Common examples include temperature changes during a day or a plant’s growth over several weeks.
折线图非常适合展示数据随时间的变化。你先描点，然后用直线连接。常见的例子包括一天中的温度变化或几周内植物的生长情况。
A pie chart shows proportions of a whole. The circle is split into sectors, and the size of each sector represents the relative size of each category. The whole circle stands for 100% of the data.
饼图展示整体的各个部分。圆被分成扇形，每个扇形的大小代表每个类别的相对大小。整个圆代表数据的100%。
You will practise reading and interpreting these graphs before designing your own. Looking closely at scales and labels is an important skill.
在自行设计图表之前，你会先练习阅读和解读这些图表。仔细观察刻度和标签是一项重要技能。
7. 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 data. In Year 7 statistics, you will work with three types of average: mean, median and mode.
平均数是一个能概括一组数据的单一数值。在七年级统计中，你将学习三种平均数：均值、中位数和众数。
The mean is calculated by adding up all the values and then dividing by how many values there are. We often write:
均值的计算方法是把所有数值相加，然后除以数值的个数。我们常写作：
Mean = sum of values ÷ number of values
The median is the middle value when the data is arranged in order. If there are two middle values, you take the mean of those two.
中位数是将数据按顺序排列后的中间值。如果有两个中间值，则取这两个值的均值。
The mode is the value that appears most often. A set of data can have one mode, more than one mode, or no mode at all if all values occur equally often.
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，或者如果所有值出现次数相同则没有众数。
8. Range and Comparing Data | 极差和数据比较
The range tells you how spread out the data is. It is found by subtracting the smallest value from the largest value.
极差告诉你数据的离散程度。它通过最大值减去最小值得到。
Range = largest value − smallest value
If one class has a test score range of 40 and another has a range of 20, the first class’s scores are more spread out. Combining an average with the range gives a better picture of a data set.
如果某班级测验分数的极差是40，另一个班级的极差是20，那么第一个班级的分数分布更分散。将一种平均数与极差结合起来能更全面地描述数据集。
When you compare two sets of data, always mention an average and the range. This makes your comparison stronger and more precise.
比较两组数据时，一定要提及一种平均数和极差。这样会让你的对比更有力、更精确。
9. Introduction to Probability | 概率简介
Probability is the branch of mathematics that deals with chance. It tells us how likely an event is to happen. Probabilities are given as numbers between 0 and 1, or as fractions and percentages.
概率是数学中处理可能性的分支。它告诉我们一个事件发生的可能性有多大。概率用0到1之间的数字表示，也可以用分数和百分数表示。
An impossible event has probability 0; a certain event has probability 1. For example, the probability of rolling a standard die and getting a 5 is 1/6. The probability of the sun rising tomorrow is 1.
不可能事件的概率为0；必然事件的概率为1。例如，掷一个普通骰子得到5的概率是1/6。明天太阳升起的概率是1。
In Year 7 you will use words like ‘even chance’, ‘likely’ and ‘unlikely’ and begin to place events on a probability scale from 0 to 1.
在七年级，你会使用诸如“均等机会”、“可能”和“不太可能”等词语，并开始将事件放在0到1的概率尺度上。
10. Real-life Applications | 实际应用
Statistics is everywhere! Sports analysts use it to compare player performance. Weather forecasters use historical data to predict tomorrow’s conditions. Businesses analyse sales figures to decide what products to stock.
统计无处不在！体育分析师用它来比较运动员的表现。天气预报员利用历史数据预测明天的天气。企业分析销售数据以决定库存哪些产品。
In medicine, statistics helps test whether new treatments work. Even your school uses data to track attendance and progress. Understanding statistics will help you make sense of the news and question claims you hear every day.
在医学上，统计有助于检验新疗法是否有效。连你的学校也使用数据来追踪出勤和进步情况。理解统计将帮助你理解新闻，并对每天听到的各种说法提出质疑。
11. Study Tips for Statistics | 统计学习技巧
Draw charts with a sharp pencil and use a ruler. Always label your axes, write a clear title and choose a sensible scale. Neatness makes your work easier to check and less likely to contain mistakes.
画图表时用尖铅笔和尺子。始终标记坐标轴、写上清晰的标题并选择合适的刻度。整洁的作业更容易检查，也更不容易出错。
When calculating the mean, double-check your addition and division. Write down all steps — this helps you spot errors and also earns marks in exams.
计算均值时，要反复检查加法和除法。写下所有步骤——这能帮助你发现错误，在考试中也能得分。
Practise explaining what a chart shows in words: ‘The bar chart shows that more students prefer cricket than hockey.’ This builds your interpretation skills.
练习用语言描述图表所展示的内容：“该条形图表明，喜欢板球的学生比喜欢曲棍球的学生多。” 这能培养你的解读能力。
12. Getting Ready for Year 7 | 为七年级做好准备
Before the term starts, practise your times tables and basic arithmetic — speed and accuracy with numbers will make statistics lessons much smoother.
在开学前，练习你的乘法表和基本算术——数字计算的速度和准确性会让统计课顺利很多。
Start noticing data in everyday life: the number of minutes you spend on different activities, the colours of cars passing your street, or the goals scored by your favourite team. Write some of these observations down in a small notebook.
开始留意日常生活中的数据：你花在不同活动上的分钟数、路过你家街道的汽车颜色，或者你最喜欢的球队的进球数。把这些观察记在一个小笔记本里。
Finally, approach statistics with a positive mindset. It is a subject that combines logic and creativity, and every new graph you draw gives you a clearer picture of the world.
最后，以积极的心态对待统计。这是一门将逻辑和创造力结合起来的学科，你绘制的每一幅新图表都能让你更清晰地了解这个世界。
Published by TutorHao | Statistics Revision Series | aleveler.com
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