IGCSE CCEA Statistics: Formula & Theorem Quick Reference | IGCSE CCEA 统计公式定理速查手册

📚 IGCSE CCEA Statistics: Formula & Theorem Quick Reference | IGCSE CCEA 统计公式定理速查手册

This handbook is a rapid revision aid for CCEA IGCSE Statistics, compiling the essential formulas and theorems you need to apply accurately in the exam. Each section presents key concepts with paired English and Chinese explanations, ready for last-minute review.

本手册是 CCEA IGCSE 统计学的快速复习资料，汇编了考试中需要准确应用的关键公式与定理。每一部分都以中英文对照的形式呈现核心概念，适合考前冲刺复习。

1. Measures of Central Tendency | 集中趋势的度量

For ungrouped data, the arithmetic mean (x̄) is the sum of all observations divided by the number of observations. The median is the central value when data are arranged in order, and the mode is the most frequently occurring value. For grouped data, class midpoints are used to approximate the mean.

对于未分组数据，算术平均数 (x̄) 是所有观测值之和除以观测值的个数。中位数是将数据排序后位于中间的值，众数是出现频率最高的数值。对于分组数据，则使用组中值来近似计算均值。

x̄ = Σx / n

If n is even, the median is the average of the n/2-th and (n/2 + 1)-th ordered values. When working with a frequency table for grouped data, multiply each class midpoint by its frequency, sum these products, and divide by the total frequency.

如果 n 为偶数，中位数是第 n/2 个和第 (n/2 + 1) 个排序值的平均数。在处理分组频数表时，将每个组中值乘以对应的频数，求和后再除以总频数。

Mean (grouped) = Σ(f × xₘ) / Σf

2. Measures of Dispersion | 离散程度的度量

The simplest measure of spread is the range, obtained by subtracting the smallest value from the largest. The interquartile range (IQR) is more robust, defined as Q₃ − Q₁. More precise measures are variance and standard deviation, which quantify variation around the mean.

最简单的离散度量是极差，即最大值减去最小值。更稳健的是四分位距 (IQR)，定义为 Q₃ − Q₁。更精确的度量是方差和标准差，用于量化数据围绕均值的波动程度。

Range = max − min

IQR = Q₃ − Q₁

For a population with mean μ and size N, the variance is σ² = Σ(x − μ)² / N and the standard deviation is σ = √[Σ(x − μ)² / N]. The sample standard deviation s uses the sample mean x̄ and divisor (n − 1) to give an unbiased estimate.

对于均值为 μ、大小为 N 的总体，方差为 σ² = Σ(x − μ)² / N，标准差为 σ = √

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