📚 WJEC Statistics Year 12 Key Terminology Quick Guide | WJEC 统计 12 年级关键术语速记指南
Mastering statistical vocabulary is the first hurdle in Year 12 WJEC Statistics. Technical terms like ‘population’, ‘parameter’, and ‘significance level’ can easily become blurred without a structured memory aid. This quick guide decodes essential terminology, pairing each concept with a clear mnemonic and a real‐world hook so you can recall definitions quickly under exam pressure.
掌握统计词汇是学习 WJEC 12 年级统计的第一关。‘总体’、‘参数’和‘显著性水平’等技术术语如果没有系统的记忆方法，很容易混淆。这篇速记指南为你拆解核心术语，为每个概念配上清晰的记忆法和现实应用场景，帮助你在考试中快速、准确地回忆定义。
1. Population vs Sample | 总体与样本
Population is the whole set of items under investigation. Sample is a subset selected from the population. Think of it like a giant pot of soup (population) and a single spoonful (sample) used to taste the whole. A census observes every member, while a sampling frame is the list from which the sample is drawn. In WJEC, ‘statistic’ refers to a quantity computed from a sample, whereas ‘parameter’ is its population counterpart.
总体是被研究对象的全体。样本是从总体中选出的一个子集。可以把总体想象成一锅巨大的汤，样本就是你用来尝味道的一勺。普查是对所有个体进行调查，而抽样框是抽取样本所用的名单。在 WJEC 中，‘统计量’由样本计算得出，‘参数’则是总体的对应真值。
2. Variable Types: Discrete and Continuous | 变量类型：离散与连续
Discrete variables can only take distinct, separate values—often counts (number of students, shoe size). Continuous variables can take any value within a range (height, time). A handy trick: ‘discrete’ sounds like ‘discreet’ items you can count one by one; ‘continuous’ implies a flowing scale you measure. Also remember categorical data (colours, exam grades A–E) lives on a nominal or ordinal scale.
离散变量只能取孤立的、可数的值，例如学生人数、鞋码。连续变量可以在一个区间内取任何值，例如身高、时间。一个简单的记忆法是：‘离散’好比你能一个一个清点的物品；‘连续’则像一把可以精细测量的尺子。另外不要忘记分类数据（颜色、考试等级A–E），它们基于名义或顺序尺度。
3. Measures of Central Tendency | 集中趋势度量
The trio mean, median and mode describe a data set’s centre. The mean is the arithmetic average, ideal for symmetric data. The median is the middle value when data are ordered—use it when outliers are present. The mode is the most frequent value. Mnemonic: ‘Mean = the one you compute, Median = the middle one, Mode = the one that appears Most’.
均值、中位数和众数这三个量描述了数据集的中心。均值是算术平均，适合对称数据。中位数是排序后位于中间的值，存在异常值时使用。众数是出现频率最高的值。记忆口诀：‘均值靠计算，中位数看中间，众数找出现最多的’。
4. Measures of Dispersion | 离散程度度量
Range (max – min), interquartile range (IQR) and standard deviation reveal data spread. IQR (Q3 – Q1) is robust against outliers, whereas standard deviation σ (population) or s (sample) measures average distance from the mean. Formula: σ² = Σ(x – μ)² / n. A small standard deviation means data cluster tightly around the mean.
极差（最大值减最小值）、四分位距 (IQR) 和标准差反映数据的离散程度。IQR (Q3 – Q1) 能抵抗异常值的影响，标准差 σ（总体）或 s（样本）则衡量数据偏离均值的平均距离。公式：σ² = Σ(x – μ)² / n。标准差越小，数据越紧密地聚集在均值周围。
5. Probability Basics: Independence and Mutual Exclusivity | 概率基础：独立与互斥
Two events are mutually exclusive if they cannot happen together: P(A ∩ B) = 0. They are independent if the occurrence of one does not affect the probability of the other: P(A ∩ B) = P(A) × P(B). Do not confuse them! Mutually exclusive events cannot be independent unless one has zero probability. A quick visual: mutually exclusive = two circles that never overlap; independent = outcome A has no influence on outcome B.
若两个事件不可能同时发生，则称为互斥：P(A ∩ B) = 0。若一个事件的发生不影响另一个事件的概率，则称为独立：P(A ∩ B) = P(A) × P(B)。千万不要混淆！除非其中一个概率为零，否则互斥事件不可能独立。直观理解：互斥 = 两个永不相交的圆；独立 = 结果A对结果B没有任何影响。
6. Conditional Probability and Bayes’ Theorem | 条件概率与贝叶斯定理
Conditional probability P(A|B) is the probability of A given that B has occurred: P(A|B) = P(A ∩ B) / P(B). Bayes’ theorem flips the condition: P(A|B) = [P(B|A) × P(A)] / P(B). In WJEC questions, set up a clear contingency table or tree diagram. The key phrase ‘given that’ always signals conditional probability.
条件概率 P(A|B) 是在已知B发生的条件下A发生的概率：P(A|B) = P(A ∩ B) / P(B)。贝叶斯定理则反转条件：P(A|B) = [P(B|A) × P(A)] / P(B)。解答 WJEC 试题时，建议画好列联表或树形图。题目中出现‘已知…’这一关键词，几乎都在提示要使用条件概率。
7. Random Variables: Expectation and Variance | 随机变量：期望与方差
A random variable X assigns a numerical value to each outcome. E(X) = Σ x·P(X = x) gives the long‐run average. Var(X) = E(X²) – [E(X)]². Always use the shortcut formula Var(X) = Σ x² P(X = x) – μ² to save time. Expectation is not necessarily a possible value—it is a centre of mass.
随机变量 X 为每个结果赋予一个数值。期望 E(X) = Σ x·P(X = x) 代表长期平均值。方差 Var(X) = E(X²) – [E(X)]²。始终使用捷径公式 Var(X) = Σ x² P(X = x) – μ² 来节省时间。期望值不一定是某个可能的取值，它更像概率分布的‘重心’。
8. Binomial Distribution Mnemonics | 二项分布速记
A binomial distribution applies when there are a fixed number of independent trials n, each with two outcomes (success/failure) and constant probability of success p. The probability function is P(X = r) = nCr pr (1 – p)n – r. Mean = np, variance = np(1 – p). Remember ‘BINS’: Binary outcomes, Independent trials, Number fixed, Same p for each trial.
适用二项分布的条件为：固定次数的独立试验 n，每次只有两种结果（成功/失败），且成功概率 p 恒定。概率函数：P(X = r) = nCr pr (1 – p)n – r。均值 = np，方差 = np(1 – p)。速记诀窍‘BINS’：Binary 两种结果，Independent 独立，Number 次数固定，Same p 相同概率。
9. Poisson Distribution Quick Tips | 泊松分布速记
The Poisson distribution models the number of events occurring in a fixed interval of time or space, with a known average rate λ. Events occur randomly and independently. P(X = r) = e–λ λr / r!. Mean = variance = λ. Use when n is large, p is small in a binomial (as an approximation). Think ‘PULSE’: Poisson Used for Low‐probability, Sporadic Events.
泊松分布用于描述在固定时间或空间区间内事件发生的次数，已知平均发生率 λ。事件随机且独立发生。概率函数：P(X = r) = e–λ λr / r!。均值 = 方差 = λ。当二项分布的 n 很大而 p 很小时，可作近似使用。记忆为‘PULSE’：Poisson Used for Low‐probability Sporadic Events（低概率零散事件）。
10. Normal Distribution and the Z-Score | 正态分布与 Z 分数
The normal distribution is a continuous, bell‐shaped curve defined by mean μ and standard deviation σ. To find probabilities, standardise using the Z‑score: Z = (X – μ) / σ. The standard normal distribution has μ = 0, σ = 1. About 68% of data lie within 1σ, 95% within 2σ, 99.7% within 3σ. Use the ’68–95–99.7′ rule for quick estimations in WJEC papers.
正态分布是一种连续型、钟形曲线，由均值 μ 和标准差 σ 决定。求概率时，通过 Z 分数标准化：Z = (X – μ) / σ。标准正态分布的均值为 0，标准差为 1。约 68% 的数据落在 1σ 内，95% 在 2σ 内，99.7% 在 3σ 内。在 WJEC 试卷中，可利用‘68–95–99.7’法则快速估算。
11. Hypothesis Testing Key Terms | 假设检验关键术语
Null hypothesis H₀ is the default assumption (e.g., coin is fair). Alternative hypothesis H₁ is what you aim to support. The significance level α (often 5%) is the probability of wrongly rejecting H₀ (Type I error). p‑value is the probability of obtaining a result at least as extreme as the observed one, assuming H₀ is true. If p‑value ≤ α, reject H₀. The critical region is the set of sample outcomes that lead to rejection. Visualise the bell curve with tails cut off by critical values.
零假设 H₀ 是默认假设（如硬币是公平的）。备择假设 H₁ 是你希望支持的陈述。显著性水平 α（常取 5%）是错误拒绝 H₀ 的概率（第一类错误）。p 值是在 H₀ 成立的条件下，得到至少和观测结果一样极端的样本结果的概率。若 p 值 ≤ α，则拒绝 H₀。拒绝域是导致拒绝 H₀ 的那些样本结果的集合。想象钟形曲线两端被临界值截去的尾部区域。
12. Correlation and Regression | 相关与回归
Product moment correlation coefficient r measures linear relationship strength between two variables. Values range from –1 to +1; r = 0 indicates no linear correlation. Regression line y = a + bx predicts y from x. The least squares method minimises the sum of squared residuals. Key check: the regression line always passes through (x̄, ȳ). Also interpret r² carefully—it represents the proportion of variance explained.
积矩相关系数 r 衡量两个变量之间线性关系的强度，取值范围 –1 到 +1；r = 0 表示没有线性相关。回归直线 y = a + bx 根据 x 预测 y。最小二乘法使残差平方和最小。关键检查点：回归直线总是通过 (x̄, ȳ)。另外要正确解读 r²，它表示被解释的方差比例。
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