Year 8 CIE Statistics: Formula & Theorem Quick Reference Handbook | Year 8 CIE 统计：公式定理速查手册

📚 Year 8 CIE Statistics: Formula & Theorem Quick Reference Handbook | Year 8 CIE 统计：公式定理速查手册

This quick reference handbook compiles the essential formulas and theorems for Year 8 CIE Statistics. It covers measures of central tendency, data representation, probability, and data interpretation. Use this guide to revise key concepts and ensure you can confidently apply them in problem-solving.

这份速查手册汇总了 Year 8 CIE 统计的核心公式与定理，涵盖集中趋势度量、数据展示、概率和数据解读。利用本指南复习关键概念，确保你能自信地应用于解题。

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1. Mean (Average) | 平均数

The mean is the sum of all data values divided by the number of values. It is often called the average.

平均数是指所有数据值的总和除以数据的个数，通常被称为均值。

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

公式：平均数 = (所有值的和) ÷ (数据的个数)

For a data set {x₁, x₂, …, xₙ}, the mean is written as: Mean = (∑xᵢ)/n, where n is the number of data values.

对于数据集 {x₁, x₂, …, xₙ}，平均数表示为：平均数 = (∑xᵢ)/n，其中 n 是数据的个数。

Example: Data: 5, 8, 11, 14, 7. Sum = 5+8+11+14+7 = 45. Number of values n = 5. Mean = 45 ÷ 5 = 9.

示例：数据：5, 8, 11, 14, 7。总和 = 5+8+11+14+7 = 45。数据个数 n = 5。平均数 = 45 ÷ 5 = 9。

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2. Median | 中位数

The median is the middle value when the data are arranged in order. For an odd number of values, the median is the central value. For an even number, it is the average of the two central values.

中位数是将数据按大小顺序排列后位于中间的值。当数据个数为奇数时，中位数就是正中那个值；当个数为偶数时，则是中间两个数的平均数。

Finding the median: Arrange data in ascending order. If n is odd, median = (n+1)/2 th value. If n is even, median = average of n/2 th and (n/2 +1)th values.

求中位数：将数据升序排列。如果 n 为奇数，中位数是第 (n+1)/2 个值。如果 n 为偶数，中位数是第 n/2 个与第 (n/2 +1) 个值的平均数。

Example (odd): Data 10, 6, 2, 8, 4 sorted: 2, 4, 6, 8, 10. n=5, median = (5+1)/2 = 3rd value = 6.

示例（奇数）：数据 10, 6, 2, 8, 4 排序后：2, 4, 6, 8, 10。n=5，中位数 = (5+1)/2 = 第3个数 = 6。

Example (even): Data 3, 9, 1, 7 sorted: 1, 3, 7, 9. n=4, median = (3+7)/2 = 5.

示例（偶数）：数据 3, 9, 1, 7 排序后：1, 3, 7, 9。n=4，中位数 = (3+7)/2 = 5。

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3. Mode | 众数

The mode is the value that occurs most frequently in a data set. There can be more than one mode (bimodal, multimodal) or no mode if all values appear equally often.

众数是数据集中出现次数最多的值。可能出现多个众数（双众数、多众数），也可能没有众数（所有值出现频率相同）。

Example: Data 2, 5, 5, 7, 5, 9. The number 5 appears three times, so mode = 5.

示例：数据 2, 5, 5, 7, 5, 9。数字 5 出现三次，所以众数 = 5。

Example (bimodal): Data 1, 2, 2, 4, 4, 6. Both 2 and 4 appear twice, so modes are 2 and 4.

示例（双众数）：数据 1, 2, 2, 4, 4, 6。2 和 4 各出现两次，因此众数为 2 和 4。

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4. Range | 极差

The range is a measure of spread, calculated as the difference between the largest and smallest values.

极差是衡量数据离散程度的一个量，等于最大值与最小值之差。

Formula: Range = Maximum value − Minimum value

公式：极差 = 最大值 − 最小值

Example: Data 12, 17, 9, 23, 15. Maximum = 23, Minimum = 9, Range = 23 − 9 = 14.

示例：数据 12, 17, 9, 23, 15。最大值 = 23，最小值 = 9，极差 = 23 − 9 = 14。

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5. Frequency Tables and Mean from a Frequency Table | 频数表与频数表求平均数

A frequency table lists data values alongside the number of times each occurs (frequency). Tally marks are used when collecting data.

频数表列出了各个数据值及其出现次数（频数）。收集数据时常用画记符号（正字）计数。

Mean from a frequency table: Multiply each data value (x) by its frequency (f), sum these products, then divide by the total frequency.

从频数表求平均数：将每个数据值 (x) 与其频数 (f) 相乘，将所有乘积求和，然后除以总频数。

Mean = ∑(f × x) / ∑f

Example: A frequency table showing score x and frequency f: x=10, f=3; x=20, f=5; x=30, f=2. Sum of f×x = 10×3 + 20×5 + 30×2 = 30 + 100 + 60 = 190. Total frequency ∑f = 3+5+2 = 10. Mean = 190/10 = 19.

示例：频数表：分数 x=10，频数 f=3；x=20，f=5；x=30，f=2。f×x 之和 = 10×3 + 20×5 + 30×2 = 30 + 100 + 60 = 190。总频数 ∑f = 3+5+2 = 10。平均数 = 190/10 = 19。

If data are grouped, use the midpoint of each class interval as x.

如果数据已分组，使用每个组区间的中点值作为 x。

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6. Probability Basics | 概率基础

Probability measures the likelihood of an event occurring. It is a number between 0 and 1 inclusive. A probability of 0 means impossible, and 1 means certain.

概率衡量某个事件发生的可能性，是一个介于 0 和 1 之间的数（含 0 和 1）。概率为 0 表示不可能发生，为 1 表示必然发生。

Formula: Probability of an event = (Number of favorable outcomes) ÷ (Total number of equally likely outcomes)

公式：事件的概率 = (有利结果的数量)

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