Year 10 Eduqas Statistics: Formula & Theorem Quick Reference Guide | Year 10 Eduqas 统计学：公式定理速查手册

📚 Year 10 Eduqas Statistics: Formula & Theorem Quick Reference Guide | Year 10 Eduqas 统计学：公式定理速查手册

This quick reference guide compiles the most important formulas and theorems you need for Year 10 Eduqas Statistics. From averages and measures of spread to probability and the binomial distribution, each section provides key concepts and symbolic notation. Keep it handy while revising or solving exam questions.

本速查手册汇总了 Year 10 Eduqas 统计学所需的最重要公式和定理。从平均数与离散度量到概率与二项分布，每节提供核心概念和符号表示法。复习或解答试题时请随时查阅。

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

The mean is the arithmetic average. For a dataset with values x₁, x₂, … xₙ, the mean x̄ = Σx / n, where Σx is the sum of all values and n is the sample size.

均值是算术平均值。对于数值 x₁, x₂, … xₙ，均值 x̄ = Σx / n，其中 Σx 是所有值的总和，n 是样本量。

The median is the middle value when data are sorted. If n is odd, the median is the (n+1)/2-th value. If n is even, it is the average of the n/2-th and (n/2+1)-th values.

中位数是数据排序后位于中间的值。若 n 为奇数，中位数为第 (n+1)/2 个数值；若 n 为偶数，则为第 n/2 个与第 (n/2+1) 个数值的平均值。

The mode is the value that appears most often. A data set may have one mode, more than one mode (bimodal, multimodal), or no mode if all values are unique.

众数是出现次数最多的值。数据集可以有一个众数、多个众数（双众数、多众数），若所有值均唯一则可没有众数。

2. Measures of Spread | 离散程度的度量

The range is the simplest measure of spread: Range = maximum value − minimum value.

极差是最简单的离散度量：极差 = 最大值 − 最小值。

The interquartile range (IQR) is the difference between the upper and lower quartiles: IQR = Q₃ − Q₁. Q₁ is the 25th percentile, Q₃ the 75th percentile. For a ranked list, positions can be found by (n+1)/4 and 3(n+1)/4; interpolate if necessary.

四分位距 (IQR) 是上四分位数与下四分位数之差：IQR = Q₃ − Q₁。Q₁ 为第 25 百分位数，Q₃ 为第 75 百分位数。对排序后的列表，位置可用 (n+1)/4 和 3(n+1)/4 确定，必要时进行插值。

The population standard deviation σ measures the average distance of values from the mean: σ = √( Σ(x − μ)² / N ), where μ is the population mean.

总体标准差 σ 衡量各数值与均值之间的平均距离：σ = √( Σ(x − μ)² / N )，其中 μ 为总体均值。

The sample standard deviation s uses n−1 in the denominator to provide an unbiased estimate: s = √( Σ(x − x̄)² / (n − 1) ).

样本标准差 s 使用分母 n−1 以给出无偏估计：s = √( Σ(x − x̄)² / (n − 1) )。

Variance is the square of the standard deviation; it is often denoted by σ² (population) or s² (sample).

方差是标准差的平方，通常记作 σ²

Published by TutorHao | Year 10 统计 Revision Series | aleveler.com

更多咨询请联系16621398022（同微信）