Year 11 OCR Statistics: Quick Reference Handbook of Formulas and Theorems | 公式定理速查手册

📚 Year 11 OCR Statistics: Quick Reference Handbook of Formulas and Theorems | 公式定理速查手册

This quick reference handbook compiles the essential formulas and theorems required for the OCR GCSE (9–1) Statistics specification. It is designed to help Year 11 students revise key statistical concepts efficiently, from measures of central tendency and dispersion to probability, correlation, regression, and index numbers. Each section presents the core formulas with concise explanations so that you can locate the needed rule swiftly during study or exam preparation.

本速查手册汇集了OCR GCSE（9–1）统计学科目所需的必备公式和定理。手册旨在帮助11年级学生高效复习关键统计概念，涵盖集中趋势与离散程度的度量、概率、相关与回归以及指数等内容。每个部分呈现核心公式并附有简明解释，方便你在学习或备考过程中快速查找所需规则。

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

The mean (average) of a data set is the sum of all values divided by the number of values. For raw data: Mean = (Σx)/n, where Σx is the total of all observations and n is the sample size. For grouped frequency tables, the mean is estimated using class midpoints: Mean ≈ (Σf x)/Σf, with x representing the midpoint of each interval and f the frequency.

均值（平均数）是一组数据中所有数值之和除以数值的个数。对于未分组数据：均值 = (Σx)/n，其中 Σx 是所有观测值的总和，n 是观测值的总个数。对于分组频数表，使用组中点估算均值：均值 ≈ (Σf x)/Σf，其中 x 是每组的组中点，f 为频数。

The median is the middle value when data are ordered. For ungrouped data with n observations, the median position is (n + 1)/2. For grouped data, linear interpolation is used within the median class. The mode is the most frequently occurring value; for grouped data it is the class with the highest frequency (modal class).

中位数是数据排序后的中间值。对于有 n 个观测值的未分组数据，中位数的位置为 (n + 1)/2。对于分组数据，在中位数组内使用线性插值。众数是出现频率最高的数值；对于分组数据，众数是频数最高的组（众数组）。

2. Measures of Dispersion | 离散程度的度量

The range is the simplest measure of spread: Range = maximum value – minimum value. It is sensitive to outliers. A more robust measure is the interquartile range (IQR), defined as IQR = Q₃ – Q₁, where Q₁ is the lower quartile and Q₃ the upper quartile. Quartiles can be found using positional formulas and interpolation for grouped data.

极差是最简单的离散度量：极差 = 最大值 – 最小值。它对异常值敏感。更稳健的度量是四分位距 (IQR)，定义为 IQR = Q₃ – Q₁，其中 Q₁ 是下四分位数，Q₃ 是上四分位数。四分位数可利用位置公式求得，分组数据需用插值。

Variance and standard deviation measure the average squared deviation from the mean. For a population, the variance is σ² = Σ(x – μ)² / N. Often, the sample variance is used: s² = Σ(x – x̄)² / (n – 1). The standard deviation is the square root of the variance: σ = √(σ²) or <

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