KS3 Edexcel Statistics: Formula & Theorem Quick Reference Guide | KS3 Edexcel 统计：公式定理速查手册

📚 KS3 Edexcel Statistics: Formula & Theorem Quick Reference Guide | KS3 Edexcel 统计：公式定理速查手册

This quick reference guide brings together the most important formulas, definitions and theorems you need for KS3 Edexcel Statistics. Use it to review the tools for collecting, displaying and analysing data, as well as the rules that underpin simple probability. Each section pairs a key idea in English with its Chinese equivalent, so you can master the content in both languages.

本速查手册汇集了 KS3 Edexcel 统计课程中最重要的公式、定义和定理。用它来回顾收集、展示和分析数据的工具，以及支撑简单概率的法则。每一节都用一个关键概念的英文和中文结对呈现，帮助你用双语掌握内容。

1. Types of Data & Sampling | 数据类型与抽样

Data can be classified as qualitative (categorical) or quantitative (numerical). Quantitative data is further split into discrete (counted, whole numbers) and continuous (measured, can take any value within a range).

数据可分为定性（分类）数据和定量（数值）数据。定量数据又分为离散型（可数，整数）和连续型（测量得到，在一个范围内可取任意值）。

Type	Description	Example
Qualitative	Non‑numerical labels	Eye colour, car brand
Quantitative discrete	Can be counted, distinct values	Number of students, shoe size
Quantitative continuous	Measured, any value in an interval	Height, time, temperature

When collecting data, we need to decide on a sampling method. A simple random sample gives every member of the population an equal chance. Other methods include systematic, stratified and convenience sampling, but in KS3 we focus on fair and representative selection.

收集数据时需要选择抽样方法。简单随机抽样让总体中每个成员有同等机会被选中。其他方法还有系统抽样、分层抽样和便利抽样，但在 KS3 阶段我们主要关注公平且具有代表性的选取方式。

A sample should be large enough to reduce bias. The population is the whole group, while the sample is the part we actually survey.

样本应足够大以减少偏差。总体是指整个群体，样本是我们实际调查的那一部分。

2. Charts & Diagrams | 图表

Data can be displayed using many types of chart. Bar charts are used for categorical or discrete data; each bar’s height shows the frequency. A bar chart usually has gaps between the bars.

数据可以用多种图表展示。条形图适用于分类或离散数据，每个条形的高度表示频数。条形图通常在条形之间有间隙。

Pie charts show proportions of a whole. The angle for each category is calculated as: (Frequency of category ÷ Total frequency) × 360˚.

饼图展示各部分占整体的比例。每个类别的扇区角度计算公式为：（该类别的频数 ÷ 总频数）× 360˚。

Line graphs are used to show trends over time, with time on the horizontal axis. Scatter graphs plot paired numerical data to look for relationships.

线形图用来显示随时间变化的趋势，时间放在横轴。散点图将成对的数值数据绘制出来，以寻找它们之间的关系。

Always label axes, give the chart a title and use a key if needed.

务必给坐标轴添加标签，为图表命名，必要时添加图例。

3. Measures of Central Tendency | 集中趋势量度

The mean is the arithmetic average. Add all the data values together, then divide by how many values there are.

平均值是算术平均数。把所有数据值相加，再除以数据的个数。

Mean = (Sum of all values) ÷ (Number of values)

The median is the middle value when the data are ordered from smallest to largest. If there is an even number of values, the median is the mean of the two middle numbers.

中位数是将数据从小到大排序后位于中间的数值。如果数据个数为偶数，则中位数是中间两个数的平均值。

The mode is the value that appears most often. A data set can have one mode (unimodal), two modes (bimodal) or many modes.

众数是出现次数最多的值。一组数据可以有一个众数（单峰）、两个众数（双峰）或多个众数。

4. Measures of Spread (Range) | 离散量度（范围）

The range measures how spread out the data are. It is the difference between the largest and smallest values.

范围量度数据的离散程度。它是最大值与最小值之差。

Range = Maximum value – Minimum value

A small range tells us the data are clustered together; a large range indicates a wide spread. The range is simple but can be affected by outliers.

范围小表明数据聚集在一起；范围大则表示数据分布很广。范围计算简单，但容易受异常值的影响。

5. Frequency Tables | 频率表

A frequency table organises data by listing each distinct value (or group) alongside its frequency – the number of times it occurs. Tally marks can help when counting.

频率表通过列出每个不同的值（或组）及其频数（出现的次数）来整理数据。计数时可以使用“正”字或画线符号来帮助统计。

From a frequency table you can find the total number of observations (sum of the frequencies) and identify the mode – the value with the highest frequency.

通过频率表可以找到观测总数（频数之和）并确定众数——频数最高的那个值。

6. Averages from Grouped Data | 分组数据平均数

When data are grouped into intervals, we cannot calculate an exact mean. Instead we estimate the mean by using the midpoint of each interval.

当数据被分成组距区间时，无法算出精确的平均值。我们可以用每个区间的中点来估计平均数。

Estimated Mean = (Σ f × m) ÷ Σ f

Here f is the frequency of the group and m is the midpoint of the group (lower bound + upper bound) ÷ 2.

其中 f 是组的频数，m 是组中点，计算公式为（下界 + 上界）÷ 2。

The modal class is the group with the highest frequency. The median interval can be found by locating the total frequency-halfth position.

众数组是频数最高的那个组。中位数所在区间可以通过找到总频数一半所在的位置来确定。

7. Probability Basics | 概率基础

Probability measures how likely an event is to happen. The scale runs from 0 (impossible) to 1 (certain), often expressed as a fraction, decimal or percentage.

概率量度事件发生的可能性。概率的尺度从 0（不可能）到 1（必然），通常用分数、小数或百分数表示。

P(Event) = Number of favourable outcomes ÷ Total number of equally likely outcomes

All outcomes together must have probabilities that sum to 1. The probability of an event not happening is 1 – P(event).

所有可能结果的概率之和必须等于 1。事件不发生的概率为 1 – P(事件发生)。

Mutually exclusive events cannot happen at the same time; for such events, P(A or B) = P(A) + P(B). In KS3 we also meet independent events, where P(A and B) = P(A) × P(B).

互斥事件不能同时发生；对于互斥事件，P(A 或 B) = P(A) + P(B)。在 KS3 阶段还会遇到独立事件，此时 P(A 和 B) = P(A) × P(B)。

8. Sample Space Diagrams | 样本空间图

A sample space is the set of all possible outcomes of an experiment. A common way to list it is a two‑way table, especially when combining two activities like rolling dice or spinning spinners.

样本空间是一次试验所有可能结果的集合。一个常用的列出方法是双向表，尤其在组合两个活动时（如掷骰子或转盘）。

For example, when two fair six‑sided dice are rolled, the sample space has 36 equally likely pairs. The probability of a specific sum can be found by counting the outcomes in the table.

例如，掷两枚公平的六面骰子时，样本空间包含 36 个等可能的结果对。某个特定总点数的概率可以通过在表格中数出对应结果求得。

P(Event) = (Number of outcomes in the event) ÷ 36

Always check that all outcomes listed are equally likely.

务必确认所列出的所有结果都是等可能的。

9. Simple Tree Diagrams | 简单树形图

Tree diagrams show sequences of events. Branches represent outcomes, with probabilities written on each branch. To find the probability of a combined event, multiply the probabilities along the relevant branches.

树形图展示事件的序列。分支代表结果，每条分支上标有概率。要计算联合事件的概率，将相关分支上的概率相乘。

P(A followed by B) = P(A) × P(B) (for independent events)

If there is more than one way for an event to happen, add the probabilities of those separate paths. Always check that the probabilities on branches from the same point add up to 1.

如果某一事件可以通过多种方式发生，就将那些独立路径的概率相加。始终检查从同一点出发的各分支概率之和是否为 1。

10. Correlation | 相关性

Correlation describes the relationship between two variables plotted on a scatter graph. Positive correlation means as one variable increases, the other also tends to increase. Negative correlation means as one increases, the other tends to decrease.

相关性描述散点图中两个变量之间的关系。正相关意味着一个变量增大时，另一个也趋向增大。负相关意味着一个变量增大时，另一个趋向减小。

No correlation occurs when there is no clear pattern. The strength of correlation can be strong, moderate or weak, depending on how close the points are to a straight line.

无明显模式时即为无相关。相关性的强度根据数据点围绕一条直线的紧密程度可分为强相关、中等相关或弱相关。

Correlation does not imply causation – a third factor may be influencing both variables.

相关性并不意味着因果关系——可能有第三个因素同时影响这两个变量。

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Published by TutorHao | Statistics Revision Series | aleveler.com

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