📚 KS3 WJEC Statistics: Core Concepts Overview | KS3 WJEC 统计：核心知识点梳理
The KS3 WJEC Statistics curriculum builds essential skills for collecting, representing, analysing and interpreting data. You will learn how to summarise information using different types of charts and numerical measures, and begin to explore the language of probability. This guide walks you through the key topics, with clear explanations in both English and Chinese to strengthen your understanding.
KS3 WJEC 统计课程帮助你建立收集、表示、分析和解读数据的核心技能。你将学习如何使用不同类型的图表和数值度量来总结信息，并开始探索概率的语言。这篇指南带你梳理所有核心知识点，每个要点都配有中英双语解释，帮助你巩固理解。
1. Types of Data | 数据类型
In statistics, data can be grouped into two main types: qualitative and quantitative. Qualitative data describes qualities or categories, such as eye colour or favourite subject. Quantitative data is numerical and can be either discrete (counted, like number of siblings) or continuous (measured, like height or mass).
在统计中，数据可以分为两大类型：定性数据和定量数据。定性数据描述质量或类别，例如眼睛的颜色或最喜欢的科目。定量数据是数值型的，可以是离散的（可数的，如兄弟姐妹的数量）或连续的（通过测量得到的，如身高或质量）。
Understanding the type of data helps you choose the right chart and the most suitable average. Discrete data often appears in bar charts, while continuous data is better shown in line graphs or histograms.
理解数据类型有助于你选择合适的图表和最合适的平均数。离散数据常用条形图表示，而连续数据更适合用折线图或直方图展示。
2. Data Collection Methods | 数据收集方法
Data can be collected through surveys, questionnaires, observations or experiments. A well-designed questionnaire uses clear, unbiased questions to avoid influencing the answers. It is important to decide whether to collect data from the whole population or a sample.
数据可以通过调查、问卷、观察或实验来收集。一份设计良好的问卷会使用清晰、无偏的问题，以避免影响回答。你需要决定是从整个总体中收集数据，还是只从样本中收集。
A sample should be representative of the population. Random sampling gives every member an equal chance of being chosen, reducing bias. In KS3, you will often work with small data sets that you can handle with tally marks.
样本应当能够代表总体。随机抽样给予每个成员被选中的均等机会，从而减少偏差。在 KS3 阶段，你通常会处理可以用计数符号记录的小型数据集。
3. Tally Charts and Frequency Tables | 计数图表与频数表
Tally charts are used to record data by hand. Each observation is marked with a stroke, and every fifth stroke is drawn across the previous four to form a group of five. This makes counting much faster and less prone to error.
计数图表用于手工记录数据。每个观测值划一道短线，每第五笔横穿前四笔形成一个五笔组。这使得计数更快，也更不容易出错。
Frequency tables list each data value or category alongside its frequency (the number of times it appears). They are the first step in organising data before drawing a chart or calculating averages.
频数表列出每个数据值或类别及其频数（出现的次数）。它是整理数据的第一步，为后续绘制图表或计算平均数做好准备。
4. Bar Charts and Pictograms | 条形图与象形图
A bar chart uses rectangular bars to represent frequencies. The height of each bar corresponds to the frequency. Bars should be of equal width and separated by gaps, as the data is categorical or discrete.
条形图用矩形长条表示频数。每个长条的高度与频数对应。长条应当等宽且彼此分离，因为数据是分类或离散的。
Pictograms use symbols or pictures to represent a certain number of items. A key must always be provided to show what one symbol stands for, for example one smiley face equals 2 students. Pictograms are visually engaging but can be less precise than bar charts.
象形图用符号或图片表示一定数量的项目。必须提供图例，说明一个符号代表多少，例如一个笑脸代表 2 名学生。象形图视觉上很吸引人，但可能不如条形图精确。
5. Pie Charts | 饼图
Pie charts display data as slices of a circle, where each slice represents a category’s proportion of the whole. The angle of each slice is found by calculating (frequency ÷ total frequency) × 360°.
饼图将数据表现为圆形的扇区，每个扇区代表一个类别占整体的比例。每个扇区的角度通过（频数 ÷ 总频数）× 360° 计算得到。
Pie charts are excellent for showing relative sizes, but they can become confusing if there are too many categories. You should always label each slice or include a legend to make the chart easy to read.
饼图非常适合显示相对大小，但如果类别过多可能会变得混乱。你应当始终为每个扇区添加标签或提供图例，使图表易于阅读。
Sector angle = (Category frequency ÷ Total frequency) × 360°
扇区角度 = （类别频数 ÷ 总频数）× 360°
6. Line Graphs and Time Series | 折线图与时间序列
Line graphs are used to show how a variable changes over time. Data points are plotted and connected by straight lines. The horizontal axis usually represents time, while the vertical axis shows the quantity being measured.
折线图用于展示一个变量如何随时间变化。数据点标出后用线段连接。横轴通常表示时间，纵轴表示被测量的量。
A time series is a sequence of data points collected at regular intervals. Trends, such as a steady increase, and seasonal patterns can be identified from the shape of the graph.
时间序列是按固定间隔收集的一系列数据点。从图形的形状可以识别趋势（如稳定增长）和季节性规律。
7. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph displays the relationship between two variables. Each point represents a pair of values. If the points tend to slope upwards, there is a positive correlation; if they slope downwards, the correlation is negative. No clear pattern suggests zero correlation.
散点图显示两个变量之间的关系。每个点代表一对数值。如果点的整体趋势向上倾斜，则存在正相关；如果向下倾斜，则为负相关。若没有明显模式，则说明零相关。
Correlation does not imply causation. Just because two variables move together does not mean one causes the other. A line of best fit can be drawn to help make predictions, but only within the range of the given data.
相关性并不意味着因果关系。两个变量一起变化并不代表一个导致另一个。可以画出最佳拟合线来帮助预测，但只能对给定数据范围内的值进行预测。
8. Stem-and-Leaf Diagrams | 茎叶图
A stem-and-leaf diagram organises numerical data while preserving the original values. The stem represents the leading digit(s), and the leaf shows the last digit. For example, 42 would have stem 4 and leaf 2.
茎叶图在保留原始数值的同时整理数值型数据。茎代表前面一位或多位数字，叶代表最后一位数字。例如，42 的茎为 4，叶为 2。
Stem-and-leaf diagrams make it easy to find the median and mode, and they show the shape of the distribution. An ordered stem-and-leaf diagram lists leaves in ascending order, which helps identify the range and quartiles.
茎叶图便于找到中位数和众数，还能展示分布形状。有序茎叶图将叶子按升序排列，这有助于识别极差和四分位数。
9. Measures of Central Tendency: Mean, Median, Mode | 集中趋势度量：平均数、中位数、众数
The mean is calculated by adding all values together and dividing by the number of values. It is the most commonly used average but can be affected by extreme values (outliers).
平均数是将所有数值相加后除以数值的个数得到的。它是最常用的平均数，但容易受到极端值（异常值）的影响。
Mean = Sum of all values ÷ Number of values
平均数 = 所有数值之和 ÷ 数值的个数
The median is the middle value when data is ordered from smallest to largest. If there are two middle values, the median is their mean. 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.
中位数是将数据从小到大排列后位于中间的值。如果有两个中间值，则中位数是它们的平均数。众数是出现次数最多的值。一个数据集可以有一个众数、多个众数（双众数）或没有众数。
10. Range and Spread | 极差与离散程度
The range measures how spread out the data is. It is simply the difference between the largest and smallest values: Range = Maximum value − Minimum value. A small range tells you the data is closely grouped; a large range indicates greater variability.
极差衡量数据的分散程度。它就是最大值与最小值之间的差：极差 = 最大值 − 最小值。极差小说明数据集中，极差大表明数据变异性更大。
The range is easy to calculate but can be misleading if there are outliers. In later study you will meet interquartile range and standard deviation, but for KS3 the range is the key measure of spread.
极差容易计算，但如果存在异常值可能会产生误导。后续学习你会接触到四分位距和标准差，但在 KS3 阶段，极差是衡量离散程度的关键指标。
11. Probability Scale and Simple Probability | 概率尺度与简单概率
Probability describes how likely an event is to happen. It is expressed as a number between 0 and 1, or as a percentage between 0% and 100%. An event that is certain has probability 1; an impossible event has probability 0.
概率描述一个事件发生的可能性大小。它用 0 到 1 之间的数字表示，或者用 0% 到 100% 的百分比表示。必然发生的事件概率为 1，不可能发生的事件概率为 0。
For equally likely outcomes, probability is found by: P(event) = Number of favourable outcomes ÷ Total number of possible outcomes. The sum of probabilities of all possible outcomes of an experiment is always 1.
对于等可能的结果，概率计算方式为：P（事件）= 有利结果的数量 ÷ 所有可能结果的总数。一个试验所有可能结果的概率之和总是 1。
P(event) = Favourable outcomes ÷ Total outcomes
P（事件）= 有利结果 ÷ 总结果
12. Interpreting Statistical Diagrams | 解读统计图表
Being able to read and interpret diagrams is just as important as creating them. Always check the title, axis labels, scales and keys. Ask yourself: what story is the data telling? Look for trends, patterns and any unusual points.
能够阅读和解读图表与制作图表同样重要。务必检查标题、轴标签、刻度和图例。问自己：这些数据在讲述什么故事？寻找趋势、规律和任何异常点。
When comparing two sets of data shown in the same type of chart, focus on differences in averages and spread. For example, one group might have a higher median but a smaller range. Always support your comments with data from the chart.
当比较同一类型图表中显示的两组数据时，应关注平均数与离散程度的差异。例如，一组的中位数可能更高但极差更小。始终用图表中的数据支撑你的评论。
The table below summarises which chart to use for different data types and purposes.
下表总结了针对不同数据类型和目的应使用哪种图表。
| Data type / 数据类型 | Recommended chart / 推荐图表 | Purpose / 目的 |
|---|---|---|
| Categorical / 分类 | Bar chart, pie chart / 条形图、饼图 | Compare frequencies or proportions / 比较频数或比例 |
| Discrete / 离散 | Bar chart, stem-and-leaf / 条形图、茎叶图 | Show distribution and find mode / 显示分布及寻找众数 |
| Continuous / 连续 | Line graph, scatter graph / 折线图、散点图 | Show trends or relationships / 展示趋势或关系 |
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