📚 Year 7 CCEA Statistics: Key Topics Summary | Year 7 CCEA 统计：核心知识点梳理
Welcome to your Year 7 CCEA statistics revision guide. This article covers the essential topics you need to know: types of data, charts and graphs, measures of average and spread, and an introduction to probability. Each concept is explained clearly with examples to help you prepare for tests and build a strong foundation in statistics.
欢迎阅读你的七年级CCEA统计复习指南。本文涵盖你需要掌握的核心主题：数据类型、图表、平均数和离散程度的度量，以及概率入门。每个概念都有清晰的解释和示例，帮助你备考并为统计打下坚实基础。
1. Types of Data | 数据类型
In statistics, data can be categorical (qualitative) or numerical (quantitative). Categorical data describes qualities, like favourite colour or eye colour. Numerical data involves numbers, such as height or number of siblings.
在统计中，数据可以是分类数据（定性）或数值数据（定量）。分类数据描述性质，例如最喜欢的颜色或眼睛颜色。数值数据涉及数字，如身高或兄弟姐妹数量。
Numerical data can be discrete (counted, e.g. number of pets) or continuous (measured, e.g. temperature). Understanding the type helps you choose the right chart and summary.
数值数据可以是离散的（可数，例如宠物数量）或连续的（可测量，例如温度）。了解数据类型有助于选择合适的图表和总结方式。
2. Collecting Data | 数据收集
Data can be collected through surveys, observations, or experiments. A survey might ask classmates about their favourite fruit. It is important to ask clear questions and record answers accurately.
数据可以通过调查、观察或实验收集。调查可能会问同学们最喜欢的水果是什么。提出清晰的问题并准确记录答案很重要。
A tally chart is often used during data collection to organise counts efficiently. Each tally mark represents one item, and groups of five make counting easier.
数据收集时常用划记表来高效整理计数。每一划代表一个项目，五个一组让计数更容易。
3. Tally Charts and Frequency Tables | 划记表与频率表
A tally chart uses tally marks to record data. The fifth mark crosses the previous four. After collecting data, you can create a frequency table showing categories and their frequencies (counts).
划记表使用划记符号记录数据。第五划会划穿前四个。收集数据后，你可以创建一个频率表，显示类别及其频率（计数）。
Example: Favourite colours – Red: 4, Blue: 7, Green: 3. This organises raw data into a clear summary.
例如：最喜欢的颜色 – 红色：4，蓝色：7，绿色：3。这样将原始数据整理成清晰的摘要。
4. Pictograms | 象形图
A pictogram represents data using pictures or symbols. Each symbol can stand for 1, 2, 5, or 10 items. A key explains what one symbol represents.
象形图用图片或符号表示数据。每个符号可以代表1、2、5或10个项目。图例说明一个符号代表什么。
When drawing a pictogram, make sure symbols are the same size and neatly arranged. Half-symbols can show partial quantities.
绘制象形图时，确保符号大小一致且排列整齐。半边符号可以用来表示部分数量。
Pictograms are easy to read and compare categories visually.
象形图易于阅读并直观地比较类别。
5. Bar Charts | 条形图
Bar charts display categorical data with rectangular bars. The height or length of each bar represents the frequency. Bars have equal width and gaps between them.
条形图用矩形条显示分类数据。每个条的高度或长度代表频率。条形宽度相等，条与条之间有间隙。
Axis labels and a title are essential. The vertical axis (y-axis) shows frequency, and the horizontal axis (x-axis) shows categories.
坐标轴标签和标题必不可少。纵轴（y轴）显示频率，横轴（x轴）显示类别。
Bar charts can be drawn horizontally or vertically. They make comparisons straightforward.
条形图可以横向或纵向绘制，使比较变得简单直观。
6. Line Graphs | 折线图
Line graphs are used to show how data changes over time. Points are plotted and connected by straight lines. The x-axis often represents time.
折线图用于显示数据随时间的变化。点被绘制并用直线连接。横轴通常代表时间。
They can reveal trends, such as temperature rising during the day. Multiple lines can compare different sets of data.
它们可以揭示趋势，比如一天中温度上升。多条线可以比较不同的数据集。
Always label axes and give a clear title. Use a ruler to join points for accuracy.
必须标注坐标轴并提供清晰的标题。用尺子连接点以确保准确性。
7. Pie Charts | 饼图
A pie chart displays data as slices of a circle. Each slice represents a category’s proportion of the total. The whole circle equals 100% or 360°.
饼图将数据显示为圆形的扇形切片。每一片代表该类别的占比。整个圆等于100%或360°。
To construct a pie chart, you calculate the angle for each category: angle = (frequency ÷ total) × 360°. Using a protractor, draw each sector.
要制作饼图，你需要计算每个类别的角度：角度 = (频率 ÷ 总数) × 360°。使用量角器绘制每个扇区。
Pie charts are excellent for showing relative sizes, but not for precise comparisons.
饼图非常适合展示相对大小，但不适合精确比较。
8. Mean | 平均数
The mean (average) is calculated by adding all values together and dividing by the number of values.
平均数（均值）通过将所有数值相加再除以数值的个数来计算。
Mean = (Sum of all data values) ÷ (Number of values)
For example, the mean of 3, 5, 7, and 9 is (3+5+7+9) ÷ 4 = 24 ÷ 4 = 6.
例如，3、5、7、9的平均数是 (3+5+7+9) ÷ 4 = 24 ÷ 4 = 6。
The mean gives a typical value but can be affected by outliers.
平均数给出了典型值，但会受到异常值的影响。
9. Median and Mode | 中位数与众数
The median is the middle value when data is ordered from smallest to largest. If there are two middle numbers, the median is their mean.
中位数是数据按从小到大排序后位于中间的值。如果有两个中间数，中位数是它们的平均值。
Example: For 2, 3, 7, 9, 11, the median is 7. For 2, 3, 7, 9, the median is (3+7)÷2 = 5.
例如：对于2、3、7、9、11，中位数是7。对于2、3、7、9，中位数是(3+7)÷2 = 5。
The mode is the value that appears most often. A data set can have one mode, more than one mode (bimodal), or no mode at all.
众数是出现频率最高的数值。数据集可以有一个众数、多个众数（双众数）或完全没有众数。
The median is not affected by extremely high or low values, making it useful for skewed data.
中位数不受极端值影响，适用于偏态数据。
10. Range | 极差
The range measures the spread of data. It is the difference between the largest and smallest values.
极差衡量数据的离散程度。它是最大值与最小值之差。
Range = Largest value – Smallest value
A small range means data values are close together; a large range shows they are spread out.
极差小说明数据值比较集中；极差大则表示数据分散。
For example, the heights (cm) 150, 155, 160, 170 have a range of 170 – 150 = 20 cm.
例如，身高（厘米）150、155、160、170的极差为170 – 150 = 20厘米。
11. Introduction to Probability | 概率初步
Probability describes how likely an event is to happen. It can be expressed in words (impossible, unlikely, even chance, likely, certain) or as a fraction between 0 and 1.
概率描述事件发生的可能性。可以用词语（不可能、不大可能、对等机会、可能、肯定）或0到1之间的分数表示。
Probability = Number of favourable outcomes ÷ Total number of outcomes
Equally likely outcomes have the same chance. The probability scale runs from 0 (impossible) to 1 (certain).
等可能的结果机会均等。概率标度从0（不可能）到1（肯定）。
For a fair six-sided die, the probability of rolling a 3 is 1/6.
对于公平的六面骰子，掷出3的概率是1/6。
12. The Statistical Enquiry Cycle | 统计调查循环
A statistical investigation follows a cycle: pose a question, collect data, analyse the data, and interpret results to draw conclusions.
统计调查遵循一个循环：提出问题、收集数据、分析数据，然后解释结果并得出结论。
Example: ‘What is the most common way Year 7 students travel to school?’ You would survey, tally, create a bar chart, find the mode, and write a statement.
例如：“七年级学生最常见的上学方式是什么？” 你会进行调查、划记、制作条形图、找出众数，并写下结论。
This cycle helps you think systematically about data and make informed decisions.
这个循环帮助你系统地思考数据并做出明智的决策。
Published by TutorHao | Statistics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
屏轩国际教育cambridge primary/secondary checkpoint, cat4, ukiset,ukcat,igcse,alevel,PAT,STEP,MAT, ibdp,ap,ssat,sat,sat2课程辅导，国外大学本科硕士研究生博士课程论文辅导