📚 A-Level CIE Statistics: Essential Terminology Memory Guide | A-Level CIE 统计：核心术语速记指南
Mastering A-Level CIE Statistics starts with a solid understanding of key terminology. This guide provides concise definitions, handy memory aids, and paired English-Chinese explanations to help you quickly recall essential terms for Paper 5 (S1) and Paper 6 (S2). Every section ends with a memory hook you can revise in the last ten minutes before an exam.
掌握 A-Level CIE 统计始于对核心术语的扎实理解。本指南提供简明定义、实用记忆技巧以及中英配对解释，助你快速回忆 Paper 5（S1）和 Paper 6（S2）的关键词汇。每一节末尾都配有一个记忆钩子，方便你在考前十分钟快速过一遍。
1. Key Statistical Notation | 常用统计符号
Statistics in Cambridge 9709 Paper 5 and Paper 6 uses two parallel families of symbols: Greek letters for population parameters and Latin letters with bars or hats for sample statistics. Reading a formula correctly starts with knowing which family a symbol belongs to.
在剑桥 9709 Paper 5 与 Paper 6 的统计中，符号分为两条并行家族：希腊字母表示总体参数，带横线或帽子的拉丁字母表示样本统计量。正确解读公式的第一步，就是分辨某个符号属于哪一家族。
μ (mu) is the population mean, the theoretical average computed from the entire population.
μ（mu）是总体均值，即从整个总体计算出的理论平均值。
x̄ (x-bar) is the sample mean, the average computed from a sample and used to estimate μ.
x̄（x-bar）是样本均值，从样本计算得到的平均值，用来估计 μ。
σ (sigma) is the population standard deviation, a measure of spread in the population.
σ（sigma）是总体标准差，衡量总体中数据的离散程度。
s is the sample standard deviation, an estimate of σ based on sample data.
s 是样本标准差，是根据样本数据对 σ 的估计。
p is the population proportion, the true fraction of successes in the population.
p 是总体比例，即总体中成功的真实比例。
p̂ (p-hat) is the sample proportion, the observed fraction of successes in a sample.
p̂（p-hat）是样本比例，即样本中观测到的成功比例。
Three further symbols appear constantly: N is the population size, n is the sample size, Σ means add up all the following terms, r is the product moment correlation coefficient, and λ (lambda) is the mean of a Poisson distribution.
还有三个符号几乎每次都会出现：N 是总体容量，n 是样本容量，Σ 表示把后面所有项相加，r 是积矩相关系数，λ（lambda）是泊松分布的均值。
| Symbol | Type | Meaning |
|---|---|---|
| μ, σ, p, λ | Parameter | 总体特征值，通常未知 |
| x̄, s, p̂, r | Statistic | 样本计算值，用于估计参数 |
Memory tip: parametric symbols are Greek (μ, σ, p, λ), while sample statistics use Latin letters with bars or hats (x̄, s, p̂). If a question asks you to estimate a parameter, your final answer must be a statistic.
记忆技巧：参数符号用希腊字母（μ、σ、p、λ），样本统计量用拉丁字母加横线或帽子（x̄、s、p̂）。若题目要求估计参数，你的最终答案必须是一个统计量。
2. Measures of Central Tendency & Location | 集中趋势与位置度量
The mean is the sum of values divided by the number of values. It is sensitive to outliers and is best used for roughly symmetric data.
均值是全部数值之和除以数值个数。它对异常值敏感，最适合用于近似对称的数据。
The formula for a raw data set is straightforward, and for grouped data you use frequencies as weights.
原始数据的公式非常直接；对于分组数据，则用频数作为权重。
x̄ = Σx ÷ n and x̄ = Σfx ÷ Σf
The median is the middle value when data are arranged in order. For an even number of values it is the mean of the two middle values, and it is resistant to outliers.
中位数是数据按顺序排列后的中间值。当数据个数为偶数时，取中间两个数的平均值；中位数不受异常值影响。
The mode is the most frequently occurring value. It is the only average suitable for categorical data, and a data set may be bimodal or have no mode at all.
众数是出现次数最多的数值。它是唯一适用于分类数据的平均数，一组数据可能有双众数，也可能没有众数。
Quartiles and percentiles describe location rather than centre: the lower quartile LQ cuts off the lowest 25% of the data, the upper quartile UQ cuts off the lowest 75%, and the interquartile range is UQ − LQ.
四分位数与百分位数描述的是位置而非中心：下四分位数 LQ 切掉最低的 25% 数据，上四分位数 UQ 切掉最低的 75%，四分位距为 UQ − LQ。
Skewness tells you which average is largest. In a positively skewed distribution the order is mode < median < mean; in a negatively skewed distribution it is reversed: mean < median < mode.
偏态告诉你哪个平均数最大。正偏（右偏）分布中顺序为众数 < 中位数 < 均值；负偏（左偏）分布中顺序相反：均值 < 中位数 < 众数。
Memory tip: the mean is the balance point of a see-saw, the median is the person standing in the middle of a queue, and the mode is the fashion item everyone is wearing.
记忆技巧：均值是跷跷板的平衡点，中位数是队伍中站在中间的人，众数是大家都在穿的那件时尚单品。
3. Measures of Dispersion | 离散程度度量
Dispersion measures how spread out the data are. The range is the largest value minus the smallest and is very sensitive to outliers, which is why the interquartile range is preferred when the data are skewed.
离散程度衡量数据的分散情况。极差是最大值减最小值，对异常值极其敏感，因此当数据偏斜时更常用四分位距。
The population variance is the mean of the squared deviations from the population mean, and the population standard deviation is its square root.
总体方差是各数值与总体均值之差的平方的平均值，总体标准差则是它的平方根。
σ² = Σ(x − μ)² ÷ N and σ = √(Σ(x − μ)² ÷ N)
For a sample, the divisor is n − 1 rather than n. This makes s² an unbiased estimator of σ², a point that examiners like to test in Paper 6.
对于样本，除数是 n − 1 而不是 n，这使 s² 成为 σ² 的无偏估计量，这一点在 Paper 6 中经常被考查。
A quicker computational form avoids calculating deviations one by one, and it is the version used inside most exam formulas involving random variables.
更快的计算形式可以避免逐个计算偏差，也是随机变量题目公式中常用的版本。
Var(X) = E(X²) − [E(X)]²
nsforms in exactly the same way, but the standard deviation is only divided by the magnitude of b, because shifting does not change spread.
编码数据题使用线性变换 y = (x − a) ÷ b。均值按同样方式变换，但标准差只需除以 |b|，因为平移不改变离散程度。
ȳ = (x̄ − a) ÷ b and sy = sx ÷ |b|
Memory tip: variance is measured in squared units, so always report the standard deviation when you describe spread in context, because it shares the units of the original data.
记忆技巧：方差的单位是原始单位的平方，因此在结合情境描述离散程度时应报告标准差，因为它与原数据单位一致。
4. Probability Language & Set Notation | 概率语言与集合符号
An experiment produces outcomes, the sample space S is the set of all possible outcomes, and an event is any subset of the sample space.
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