A-Level WJEC Statistics: Quick Memorisation Guide for Key Terms | A-Level WJEC 统计：词汇术语速记指南

📚 A-Level WJEC Statistics: Quick Memorisation Guide for Key Terms | A-Level WJEC 统计：词汇术语速记指南

Mastering the vocabulary of statistics is half the battle in A-Level WJEC Mathematics. This guide breaks down essential terms by topic, pairing each with a clear English definition and a memorable trick – from acronyms to visual hooks – so you can recall them instantly in the exam. Whether it is discrete random variables, hypothesis tests, or correlation, these bite-sized explanations will strengthen your statistical fluency.

掌握统计学术语是攻克 A-Level WJEC 数学的关键。本指南按主题拆解核心词汇，每个术语都配有清晰的英文定义和记忆妙招——从首字母缩略词到视觉联想，帮助你在考试中即时回忆。无论是离散随机变量、假设检验还是相关性，这些精炼的讲解都将提升你的统计语言流利度。

1. Data Types & Sampling | 数据类型与抽样

Qualitative data are non-numerical categories like colour or gender. Think ‘Quality not Quantity’.

定性数据是非数值类别，如颜色或性别。联想“定性无数字”。

Quantitative data are numerical measurements. They split into discrete (countable, e.g. number of students) and continuous (measurable, e.g. height). Remember: if you can count it, it’s discrete; if you need a ruler, it’s continuous.

定量数据是数值测量。分为离散型（可数，如学生人数）和连续型（可测，如身高）。口诀：能数就离散，上尺就连续。

Random sample gives every member of the population an equal chance of being chosen. Use the acronym RANSOM – Random, All, No bias, Simple.

随机样本使总体中每个成员被选中的机会相等。用首字母缩略 RANSOM 记忆：Random（随机），All（全员），No bias（无偏），Simple（简单）。

Census collects data from the entire population. ‘Census = Complete coverage’.

普查从整个总体收集数据。“普查 = 全面覆盖”。

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

Mean is the arithmetic average. For a frequency table, x̄ = Σfx / Σf. Link ‘mean’ with ‘average joe’ – the most typical value.

均值是算术平均数。对于频数表，x̄ = Σfx / Σf。把“均值”与“平均人”联系——最典型的值。

Median is the middle value when data are ordered. If n is odd, it’s the (n+1)/2 th value. Use the word ‘media’ – in the middle of a newspaper.

中位数是数据排序后的中间值。若 n 为奇数，则是第 (n+1)/2 个值。借用“媒体”一词——处于中心位置。

Mode is the most frequent value. Think ‘Mode = Most often’. For grouped data, the modal class has the highest frequency density.

众数是出现最频繁的值。联想“众”即多数。对于分组数据，众数区间频数密度最高。

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3. Measures of Dispersion | 离散程度的度量

Range = maximum − minimum. Quick and dirty spread. Remember ‘Range Rover’ travels far.

极差 = 最大值 − 最小值。快速粗略的离散度。想象“路虎揽胜”跑得远。

Interquartile range (IQR) = Q₃ − Q₁. It resists outliers. ‘IQR cuts off the extremes’.

四分位距 (IQR) = Q₃ − Q₁。它能抵抗异常值。“IQR 切掉极端”。

Variance (σ²) measures average squared deviation from the mean. Formula: Σ(x − μ)² / n or Σfx² / Σf − x̄² for frequency data. Mnemonic: ‘Variance squares the distance’.

方差 (σ²) 衡量与均值的平均平方偏差。公式：Σ(x − μ)² / n 或频数表用 Σfx² / Σf − x̄²。记忆：“方差是离差平方的均值”。

Standard deviation (σ) is the square root of variance. It returns to original units. S = √variance. Picture a ‘standard’ ruler – it measures spread in the same units as the data.

标准差 (σ) 是方差的平方根，回到原始单位。S = √方差。想象一把“标准”尺——用数据的单位度量离散。

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4. Probability Fundamentals | 概率基础

Sample space is the set of all possible outcomes of an experiment. Think of a ‘space’ ship carrying all possibilities.

样本空间是实验所有可能结果的集合。想象一艘“太空船”载着所有可能性。

Mutually exclusive events cannot happen at the same time. P(A ∩ B) = 0. ‘Mutually ex-clusive’ = exclude each other.

互斥事件不能同时发生。P(A ∩ B) = 0。“互斥”即互相排斥。

Independent events have no influence on each other. P(A ∩ B) = P(A) × P(B). Link: ‘Independence’ like two independent countries – one’s action doesn’t affect the other.

独立事件彼此无影响。P(A ∩ B) = P(A) × P(B)。联想：像两个独立国家，一方的行为不影响另一方。

Conditional probability P(A|B) = P(A ∩ B) / P(B). It’s probability of A given B. The vertical bar ‘|’ means ‘under the condition of’.

条件概率 P(A|B) = P(A ∩ B) / P(B)，表示在 B 发生的条件下 A 发生的概率。竖线“|”意为“在……条件下”。

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5. Discrete Random Variables | 离散随机变量

A random variable (X) is a variable whose value is a numerical outcome of a random phenomenon. ‘Random + Variable = uncertain number’.

随机变量 (X) 是数值结果由随机现象决定的变量。“随机 + 变量 = 不确定的数字”。

The probability mass function (p.m.f.) P(X = x) lists probabilities for each possible value. Sum of all probabilities = 1. Visualise a ‘mass’ of probability pieces that together make a whole.

概率质量函数 (p.m.f.) P(X = x) 列出每个可能值的概率。所有概率之和 = 1。想象“质量”块拼成整体。

For E(X) (expected value), use Σ xP(X = x). It’s the long-run average. Think ‘Expectation = mean of distribution’.

E(X)（期望） = Σ xP(X = x)，是长期平均值。联想“期望即分布的均值”。

Var(X) = E(X²) − [E(X)]². The ‘shortcut formula’ avoids building a deviation table. Remember: variance = ‘mean of square minus square of mean’.

Var(X) = E(X²) − [E(X)]²，快捷公式避免构造偏差表。记“方差 = 平方的均值 − 均值的平方”。

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6. Binomial & Poisson Distributions | 二项分布与泊松分布

The Binomial distribution B(n, p) counts successes in n independent trials, each with probability p. Conditions: fixed n, independence, same p, binary outcome. Acronym: FISB – Fixed trials, Independent, Same probability, Binary.

二项分布 B(n, p) 计算 n 次独立试验中成功的次数，每次成功概率为 p。条件：固定 n、独立、相同 p、二元结果。首字母：FISB（Fixed, Independent, Same, Binary）。

Mean E(X) = np, variance = np(1−p). Mnemonic: ‘n times p for the mean, then multiply by (1−p) for variance’.

均值 E(X) = np，方差 = np(1−p)。记忆：“均值就是 n 乘 p，方差再乘 (1−p)”。

The Poisson distribution Po(λ) models rare events occurring randomly in a fixed interval. Conditions: events occur singly, at a constant rate, independently. Use the word ‘PRISM’ – Poisson, Rate constant, Independent, Single events, Memoryless.

泊松分布 Po(λ) 模拟固定区间内随机发生的稀有事件。条件：事件单独发生、恒定速率、独立。用“PRISM”帮助记忆（Poisson, Rate constant, Independent, Single, Memoryless）。

Mean = variance = λ. Think ‘Poisson is perfectly balanced – mean equals variance’.

均值 = 方差 = λ。记住“泊松完美平衡——均值等于方差”。

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7. Continuous Random Variables & Normal Distribution | 连续随机变量与正态分布

A probability density function (p.d.f.) f(x) satisfies f(x) ≥ 0 and total area under curve = 1. Probabilities are areas. Visualise a density curve as a flat ‘pancake’ of probability spread over the x-axis.

概率密度函数 (p.d.f.) f(x) 满足 f(x) ≥ 0 且曲线下总面积 = 1。概率即面积。将密度曲线想象成平摊在 x 轴上的“概率煎饼”。

The Normal distribution N(μ, σ²) is bell-shaped, symmetric about mean μ. Key property: 68% of data within 1σ, 95% within 2σ, 99.7% within 3σ. Remember ’68-95-99.7 rule’ as an empirical telephone number.

正态分布 N(μ, σ²) 呈钟形，关于均值 μ 对称。关键性质：68% 数据落在 1σ 内，95% 在 2σ，99.7% 在 3σ。把“68-95-99.7 规则”记作经验电话号码。

To standardise, Z = (X − μ) / σ. This gives Z ~ N(0,1). Think ‘Z-score = standard deviations away from mean’.

标准化：Z = (X − μ) / σ，得到 Z ~ N(0,1)。记忆“Z 分数 = 离均值几个标准差”。

When using tables, remember the Normal table gives P(Z < z). For P(Z > z), use 1 − table value. ‘Table always gives left-tail area’.

查表时记住正态分布表给出 P(Z < z)。求 P(Z > z) 用 1 − 表值。“表永远给左尾面积”。

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8. Sampling & Estimation | 抽样与估计

The sample mean x̄ is an unbiased estimator of the population mean μ. The distribution of x̄ has mean μ and standard error σ/√n. ‘Standard error’ sounds like ‘standard deviation of the error’ – it shrinks as n grows.

样本均值 x̄ 是总体均值 μ 的无偏估计。x̄ 的分布均值为 μ，标准误为 σ/√n。“标准误”听上去像“误差的标准差”——它随 n 增大而缩小。

The Central Limit Theorem (CLT) says that for large n, the distribution of x̄ becomes approximately normal regardless of the population shape. The magic number often used is n ≥ 30. Chant: ‘CLT, thirty sets you free’.

中心极限定理 (CLT) 指出，当 n 大时，无论总体形状，x̄ 的分布近似正态。常用神奇数字 n ≥ 30。口诀：“CLT，三十就自由”。

A confidence interval for μ (with known σ) is x̄ ± z* × σ/√n. The z* value comes from the standard normal. For 95% CI, z* = 1.96. Remember: ‘Estimator plus/minus a few standard errors’.

置信区间（σ 已知）为 x̄ ± z* × σ/√n。z* 值来自标准正态。95% CI 对应 z* = 1.96。记忆：“估计值加减几个标准误”。

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9. Hypothesis Testing | 假设检验

A null hypothesis H₀ is the statement being tested, usually ‘no effect’ or ‘no difference’. Think ‘H₀ = Ho-hum, nothing happening’.

零假设 H₀ 是被检验的陈述，通常为“无效应”或“无差异”。联想“H₀ = 哼，没啥事”。

The alternative hypothesis H₁ is what you suspect is true. One-tailed tests use < or >; two-tailed uses ≠. Picture H₁ as a hungry shark – it goes after the direction it expects.

备择假设 H₁ 是你怀疑为真的说法。单尾检验用 < 或 >；双尾用 ≠。想象 H₁ 是饥饿的鲨鱼——朝着预期的方向去。

The test statistic is a value calculated from the sample to compare with a critical value. For a binomial test, it’s the number of successes. For a Normal test, it’s the Z-score.

检验统计量 是根据样本计算出来与临界值比较的数值。二项检验中是成功次数。正态检验中是 Z 分数。

The p-value is the probability of obtaining a result at least as extreme as the observed, given H₀ is true. Small p (typically < 0.05) leads to rejecting H₀. Mnemonic: 'If p is low, H₀ must go'.

p 值 是在 H₀ 为真的条件下，得到至少与观测结果一样极端的概率。p 小（通常< 0.05）则拒绝 H₀。口诀：“p 值低，H₀ 走你”。

Significance level α is the threshold probability for rejecting H₀. Common α = 0.05. ‘Alpha sets the cutoff for how much error you’ll accept’.

显著性水平 α 是拒绝 H₀ 的概率阈值。常用 α = 0.05。“α 设定了你愿意接受多少错误”。

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10. Correlation & Regression | 相关与回归

The Pearson product-moment correlation coefficient r measures linear association between two variables. r lies between −1 and +1. Think ‘r is rude – it tells you how closely variables stick to a line’.

皮尔逊积矩相关系数 r 衡量两变量间的线性关联。r 介于 −1 和 +1 之间。联想“r 很直率——它告诉你数据点贴着线的紧密程度”。

r = 1 means perfect positive correlation; r = −1 perfect negative; r = 0 no linear correlation. Memory trick: ‘1 = all points line up, 0 = cloud’.

r = 1 完全正相关；r = −1 完全负相关；r = 0 无线性相关。记忆：“1 就是全部点成线，0 就是一团云”。

The regression line y = a + bx is the least-squares line where b = Sxy / Sxx and a = ȳ − bx̄. Sxy is the covariance of x and y. ‘b is the slope – b for best-fit’.

回归线 y = a + bx 是最小二乘线，其中 b = Sxy / Sxx，a = ȳ − bx̄。Sxy 是 x 与 y 的协方差。“b 是斜率——b 代表最佳拟合”。

Interpolation uses the regression line inside the data range; extrapolation goes outside. ‘Interpolation is safer; extrapolation can be dangerous – like driving beyond the headlights’.

内插 在数据范围内使用回归线；外推 超出范围。“内插更安全；外推可能有危险——好比开车超过车灯照射范围”。

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11. Quick Recap with Memory Cards | 闪卡速记总览

Term (English) | 术语（中文）	Memory Hook | 记忆钩子
Standard error | 标准误	σ/√n shrinks as n grows | n 大误差小
CLT | 中心极限定理	n ≥ 30 → approx normal | n≥30 则近似正态
Variance shortcut | 方差快捷公式	E(X²) − [E(X)]²
p-value | p 值	If p low, H₀ go | p 低则拒 H₀
r correlation | 相关系数 r	1 perfect, 0 cloud | 1 成线，0 成云
Z-score | Z 分数	Number of σ from μ | 离 μ 几个标准差

Keep this table on your study wall – a quick glance reinforces the links between symbols and meaning.

把这张表贴在书桌墙上——扫一眼就能强化符号与意义的联系。

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12. Exam Tips for Terminology | 考试术语应对技巧

WJEC often asks you to define a term before using it. Always give a precise statistical definition, not a casual one. For example, ‘the median is the value that splits an ordered dataset into two halves’.

WJEC 常要求在使用术语前先定义。务必给出精确的统计定义，而非随意描述。例如，“中位数是将有序数据集分成两半的值”。

For full marks, include context – ‘the p-value of 0.03 means there is a 3% probability of obtaining such an extreme result if the null hypothesis were true’.

要拿满分，需包含语境——“p 值为 0.03 意味着若零假设成立，得到如此极端结果的概率为 3%”。

Practice writing definitions in both English and Chinese to cement bilingual understanding, which helps in decoding wordy exam questions.

练习用中英双语写出定义，强化双语理解，这有助于解读试卷上冗长的题目。

Use these mnemonic strategies actively: create your own silly sentences or acronyms. Personalised hooks are the strongest memory aids.

积极使用这些记忆策略：创造你自己的滑稽句子或首字母缩写。个性化的钩子是最强的记忆辅助。

Published by TutorHao | Statistics Revision Series | aleveler.com

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