A-Level CCEA Psychology: Formulae and Theorems Quick Reference Handbook | A-Level CCEA 心理学：公式定理速查手册

📚 A-Level CCEA Psychology: Formulae and Theorems Quick Reference Handbook | A-Level CCEA 心理学：公式定理速查手册

This quick reference handbook provides essential statistical formulae and key theorems required for the A-Level CCEA Psychology specification. Mastering these will enhance your ability to analyse data in research methods and interpret findings accurately.

本速查手册提供 A-Level CCEA 心理学课程所需的基本统计公式与关键定理。掌握这些内容将提升你在研究方法中分析数据并准确解释研究结果的能力。

1. Descriptive Statistics Overview | 描述统计概览

Descriptive statistics summarise and organise raw data so that patterns become apparent. They include tables, graphs, and summary measures such as central tendency and dispersion.

描述统计用于总结和整理原始数据，以便显现规律。它们包括表格、图表以及集中趋势和离散程度等汇总测量。

2. Measures of Central Tendency | 集中趋势测量

The three main measures are the mean, median, and mode. The mean, or arithmetic average, is calculated as x̄ = Σx / n, where Σx is the sum of all scores and n is the number of scores. The median is the middle value when data are ordered; for an odd number of scores it is the (n+1)/2th value, and for an even number it is the average of the two middle values. The mode is the most frequently occurring score.

三种主要测量指标是平均数、中位数和众数。平均数即算术平均值，计算公式为 x̄ = Σx / n，其中 Σx 是所有分数的总和，n 是分数的个数。中位数是排序后最中间的数值；当分数个数为奇数时，第 (n+1)/2 个数值即为中位数；当为偶数时，取中间两个数值的平均值。众数是出现频率最高的分数。

3. Measures of Dispersion: Range and Interquartile Range | 离散测量：极差与四分位距

Dispersion indicates how spread out the data are. The range is the difference between the highest and lowest values: Range = Maximum − Minimum. The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁): IQR = Q₃ − Q₁. The IQR is less affected by outliers than the range.

离散程度反映数据的分散情况。极差是最大值与最小值的差：极差 = 最大值 − 最小值。四分位距（IQR）是上四分位数（Q₃）与下四分位数（Q₁）的差值：IQR = Q₃ − Q₁。四分位距受异常值的影响小于极差。

4. Standard Deviation and Variance | 标准差与方差

The standard deviation measures the average distance of each score from the mean. For a sample, it is

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