A-Level Mathematics: Core Concepts of Measures of Dispersion | A-Level 数学：离散程度度量核心概念

📚 A-Level Mathematics: Core Concepts of Measures of Dispersion | A-Level 数学：离散程度度量核心概念

In statistics, measures of dispersion describe how spread out a set of data is. While measures of central tendency such as the mean, median, and mode give us a typical value, they tell us nothing about the variability within the data. Two datasets can have the same mean yet look completely different — one might be tightly clustered around the centre, while the other could be widely scattered. This article covers the core concepts of dispersion that you need for A-Level Mathematics: range, interquartile range, variance, standard deviation, mean absolute deviation, coefficient of variation, and the effect of linear transformations.

在统计学中，离散程度度量描述一组数据的分散程度。均值、中位数和众数等集中趋势度量给出一个典型值，但它们无法告诉我们数据内部的变异性。两组数据可以有相同的均值，却呈现完全不同的分布——一组可能紧密聚集在中心附近，而另一组可能极为分散。本文将涵盖 A-Level 数学中离散程度度量的核心概念：极差、四分位距、方差、标准差、平均绝对偏差、变异系数以及线性变换的影响。

1. What is Dispersion and Why It Matters | 什么是离散程度及其重要性

Dispersion, also called spread or variability, measures how far individual data points are from the centre of the distribution. It is essential for comparing datasets beyond their averages and for assessing reliability. A smaller dispersion indicates that the data are clustered closely around the mean, suggesting greater consistency; a larger dispersion indicates instability and a wider spread of values.

离散程度（也称散布

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