📚 Pre-U OCR Statistics: Glossary & Terminology Quick-Memorisation Guide | Pre-U OCR 统计：词汇术语速记指南
Welcome to your essential quick-reference guide for mastering statistical vocabulary in the OCR Pre-U Statistics course. Whether you are a native English speaker or learning statistical concepts bilingually, this guide pairs each key term with a concise explanation and memory-friendly cues to help you recall definitions, notation, and relationships effortlessly.
欢迎查阅这本关键速查指南，它将帮助您掌握 OCR Pre-U 统计课程中的统计词汇。无论您是以英语为母语还是双语学习统计概念，本指南都将关键术语与简洁的解释和助记提示配对，让您轻松回忆起定义、符号和关系。
1. Population and Sample | 总体与样本
A population is the entire set of items or individuals of interest. A sample is a subset of the population selected for study. The population parameter (e.g., population mean μ) is a fixed, usually unknown numerical summary, whereas a statistic (e.g., sample mean x̄) is a value computed from the sample used to estimate the parameter.
总体是所关注的全部项目或个体的集合。样本是从总体中选出的用于研究的子集。总体参数（如总体均值 μ）是一个固定但通常未知的数值概括，而统计量（如样本均值 x̄）是从样本计算出的数值，用于估计参数。
Memory tip: ‘Population = Parameter’; ‘Sample = Statistic’. Both pairs start with the same letter. The Greek letter μ symbolises the unknown true mean, while x̄ (x-bar) reminds us we are averaging over a sample.
记忆提示：“总体（Population）=参数（Parameter）”，“样本（Sample）=统计量（Statistic）”。每对单词开头字母相同。希腊字母 μ 象征未知的真实均值，而 x̄（x 一杠）提醒我们是在对样本求平均。
2. Types of Data and Variables | 数据与变量的类型
Categorical (qualitative) data represent characteristics like colour or type, often summarised by frequencies. Numerical (quantitative) data are numbers, further divided into discrete (countable, e.g., number of students) and continuous (measurable, e.g., height). Variables can also be nominal (unordered categories), ordinal (ordered categories), interval (no true zero), or ratio (true zero exists).
分类（定性）数据表示颜色或类型等特征，通常用频数汇总。数值（定量）数据是数字，进一步分为离散型（可计数，如学生人数）和连续型（可测量，如身高）。变量还可以分为名义的（无序类别）、顺序的（有序类别）、间隔的（无真正零点）或比率的（存在真正零点）。
Quick recall: ‘NOIR’ – Nominal, Ordinal, Interval, Ratio. Think of the shades of measurement scales.
快速记忆：“NOIR”——名义、顺序、间隔、比率。联想到测量尺度的层次。
3. Measures of Central Tendency | 集中趋势的度量
The mean (x̄ = Σxᵢ / n) is the arithmetic average, sensitive to outliers. The median is the middle value when data are ordered, robust to skewness. The mode is the most frequent value. In a symmetric distribution, mean = median = mode; in a right‑skewed distribution, mean > median > mode; in left‑skewed, mean < median < mode.
均值（x̄ = Σxᵢ / n）是算术平均值，对异常值敏感。中位数是数据排序后的中间值，对偏态稳健。众数是最频繁出现的值。在对称分布中，均值 = 中位数 = 众数；在右偏分布中，均值 > 中位数 > 众数；在左偏分布中，均值 < 中位数 < 众数。
Memory: ‘Mean is mean to outliers, Median is merciful.’ Also ‘In a right‑skew, the mean gets pulled to the right.’
记忆：“均值对异常值很苛刻，中位数却很宽容。”还有“在右偏分布中，均值被向右拉”。
4. Measures of Dispersion | 离散的度量
Range = max – min. Interquartile range (IQR) = Q₃ – Q₁, robust to outliers. Variance σ² (population) or s² (sample) measures average squared deviation from the mean. Standard deviation σ or s is the square root of variance, expressed in original units. The sample standard deviation formula uses n−1 denominator (Bessel’s correction) to produce an unbiased estimate of σ.
极差 = 最大值 – 最小值。四分位距 (IQR) = Q₃ – Q₁，对异常值稳健。方差 σ²（总体）或 s²（样本）衡量与均值的平方偏差的平均值。标准差 σ 或 s 是方差的平方根，以原始单位表示。样本标准差的公式使用 n−1 分母（贝塞尔校正），以得到 σ 的无偏估计。
Mnemonics: ‘IQR covers the middle 50%’ and ‘Dividing by n−1 gives us freedom to estimate.’ Variance is hard to interpret; standard deviation brings it back to scale.
助记：“IQR 覆盖中间 50% 的数据”，以及“除以 n−1 给了我们估计的自由度”。方差难以解读，标准差恢复为原始尺度。
5. Probability Fundamentals | 概率基础
Probability P(A) of an event A is a number between 0 and 1. Mutually exclusive events cannot occur together: P(A∩B) = 0. Independent events satisfy P(A∩B) = P(A)P(B). Conditional probability P(A|B) = P(A∩B)/P(B). The complement rule: P(A’) = 1 − P(A). Permutations (order matters) and combinations (order irrelevant) are used for counting outcomes.
概率 P(A) 是事件 A 发生的可能性，介于 0 和 1 之间。互斥事件不能同时发生：P(A∩B) = 0。独立事件满足 P(A∩B) = P(A)P(B)。条件概率 P(A|B) = P(A∩B)/P(B)。补集规则：P(A’) = 1 − P(A)。排列（顺序重要）和组合（顺序无关）用于计算结果的数量。
Think ‘mutually exclusive cannot coexist’ and ‘independent means multiply’. For conditional probability, the given event B becomes the new sample space.
想一想“互斥不能共存”，“独立相乘”。对于条件概率，给定的事件 B 成为新的样本空间。
6. Random Variables and Expectation | 随机变量与期望
A random variable X assigns a numerical value to each outcome of a random experiment. Discrete random variables have a probability mass function P(X = x). Continuous random variables have a probability density function f(x); probabilities are found by areas under the curve. Expected value E(X) = Σ x·P(X=x) for discrete, or ∫ x f(x) dx for continuous. Variance Var(X) = E(X²) − [E(X)]².
随机变量 X 为随机试验的每个结果赋予一个数值。离散随机变量具有概率质量函数 P(X = x)。连续随机变量具有概率密度函数 f(x)；概率由曲线下方面积求得。期望值 E(X) = Σ x·P(X=x)（离散），或 ∫ x f(x) dx（连续）。方差 Var(X) = E(X²) − [E(X)]²。
Memory: ‘Discrete = dots (mass), continuous = curve (density).’ The variance formula ‘mean of squares minus square of mean’ is universal.
记忆：“离散 = 点（质量），连续 = 曲线（密度）”。方差公式“平方的均值减去均值的平方”是通用的。
7. Common Probability Distributions | 常见概率分布
Binomial distribution B(n, p): number of successes in n independent trials, each with success probability p. Mean = np, variance = np(1−p). Conditions: fixed n, independent trials, constant p, two outcomes. Normal distribution N(μ, σ²): symmetric, bell‑shaped, defined by mean and standard deviation. The standard normal Z ~ N(0,1) uses z‑scores. Poisson distribution Po(λ): counts of events in a fixed interval, mean = variance = λ. Remember ‘Poisson means equal mean and variance’.
二项分布 B(n, p)：在 n 次独立试验中成功的次数，每次成功概率为 p。均值 = np，方差 = np(1−p)。条件：固定 n，独立试验，恒定 p，两种结果。正态分布 N(μ, σ²)：对称的钟形曲线，由均值和标准差定义。标准正态 Z ~ N(0,1) 使用 z 分数。泊松分布
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