📚 Vocabulary & Terminology Quick-Reference Guide | 词汇术语速记指南
Mastering statistical vocabulary is the first step to acing Pre-U WJEC Statistics. This guide pairs each essential term with a memory aid and its Chinese equivalent, so you can build bilingual fluency and deep understanding at the same time.
掌握统计学词汇是在 Pre-U WJEC 统计考试中取得高分的第一步。本指南为每个核心术语搭配了记忆窍门和中文对应，让你同时建立起双语理解和深层记忆。
1. Measures of Central Tendency | 集中趋势的度量
Mean – the sum of all data values divided by the number of values, represented by x̄ for a sample and μ for a population.
均值 – 所有数据值之和除以数据个数，样本均值记为 x̄，总体均值记为 μ。
Memory tip: "Mean" rhymes with "between" – it sits in the middle, balancing the dataset. Think of μ as the Greek ‘m’ for ‘middle’.
记忆窍门：“Mean” 和 “between” 押韵，它位于数据集的中间。μ 像希腊文的 “m”，代表 “middle”（中间）。
Median – the middle value when data are ordered. Notation: Q₂ or M.
中位数 – 数据排序后的中间值。符号：Q₂ 或 M。
Memory tip: "Median" shares a root with "medium" – the one in the middle, like the central reservation on a dual carriageway.
记忆窍门：“Median” 与 “medium” 同源，就像公路的中央分隔带，总是在中间。
Mode – the most frequently occurring value(s). A dataset can be unimodal, bimodal or have no mode.
众数 – 出现频率最高的值。数据集可以是单峰、双峰或无众数。
Memory tip: "Mode" sounds like "most" – the value that appears most often.
记忆窍门：“Mode” 发音像 “most”，出现次数最多的值。
2. Measures of Dispersion | 离散程度的度量
Range = maximum − minimum. It gives a quick sense of spread but ignores everything in between.
极差 = 最大值 − 最小值。它能快速反映波动范围，但忽略了中间所有数据。
Memory tip: "Range" is how far your data "ranges" from low to high.
记忆窍门：“Range” 是你的数据从低到高 “range”（延伸）的范围。
Interquartile Range (IQR) = Q₃ − Q₁. It measures the spread of the middle 50% of data, robust to outliers.
四分位距 (IQR) = Q₃ − Q₁。它衡量中间 50% 数据的离散程度，不受异常值影响。
Memory tip: "Inter" means "between", "quartile" refers to quarters – so IQR is the distance between the first and third quarters.
记忆窍门：“Inter” 意为“之间”，“quartile” 指四分之一，所以 IQR 是第一和第三四分位之间的距离。
Variance – the average of the squared deviations from the mean. Sample variance s² = [Σ(xᵢ − x̄)²]/(n−1). Population variance σ² = [Σ(xᵢ − μ)²]/N.
方差 – 各数据与均值之差的平方的平均值。样本方差 s² = [Σ(xi − x̄)²]/(n−1)，总体方差 σ² = [Σ(xi − μ)²]/N。
Memory tip: "Variance" = "vari-" (variation) + "-ance" (state). It’s the state of how much things vary, squared to avoid negatives.
记忆窍门：“Variance” = “vari-” （变化）+ “-ance” （状态）。是变化程度的状态，平方是为了避免负值。
Standard Deviation – the square root of variance, bringing it back to the original units. s = √s², σ = √σ².
标准差 – 方差的平方根，使得单位与原始数据一致。s = √s², σ = √σ²。
Memory tip: The "standard" deviation is the standard way to report spread in the same units as the data.
记忆窍门：“Standard” 偏差是用与数据相同单位报告离散程度的“标准”方式。
3. Quartiles and Percentiles | 四分位数与百分位数
Quartiles split ordered data into four equal parts. Q₁ (lower quartile) is the 25th percentile, Q₂ (median) is the 50th, Q₃ (upper quartile) is the 75th.
四分位数 将有序数据分成四等份。Q₁（下四分位数）是第 25 百分位数，Q₂（中位数）是第 50 百分位数，Q₃（上四分位数）是第 75 百分位数。
Memory tip: Think of a "quarter" coin – 25 cents – Q₁ is at 25%, Q₃ at 75%.
记忆窍门：想想 “quarter” 硬币代表 25 美分，Q₁ 在 25%，Q₃ 在 75%。
Percentile – the value below which a given percentage of observations fall. The kth percentile Pk has k% of data below it.
百分位数 – 给定百分比的数据所落在的值。第 k 百分位数 Pk 表示 k% 的数据小于它。
Memory tip: "Percent" + "ile" – just think "per hundred position".
记忆窍门：“Percent” + “ile”，就是“每一百的位置”。
4. Probability Fundamentals | 概率基础
Sample space (S) – the set of all possible outcomes of an experiment. Denoted by S or Ω.
样本空间 (S) – 随机试验所有可能结果的集合。用 S 或 Ω 表示。
Memory tip: "Sample" means you take a sample of all that could happen; "space" is the universe of outcomes.
记忆窍门：“Sample” 表示你取所有可能发生的情况的样本，“space” 是所有结果的宇宙。
Event – a subset of the sample space. Notation: capital letters like A, B.
事件 – 样本空间的子集。用大写字母如 A、B 表示。
Memory tip: An "event" is something that can "e-ventually" happen.
记忆窍门：“Event” 是最终可能“e-ventually”发生的事情。
Mutually exclusive events – events that cannot happen at the same time. P(A ∩ B) = 0.
互斥事件 – 不能同时发生的事件。P(A ∩ B) = 0。
Memory tip: "Mutually exclusive" = they exclude each other, like light and darkness.
记忆窍门：“Mutually exclusive” = 互相排斥，就像光亮与黑暗。
Independent events – the occurrence of one does not affect the probability of the other. P(A ∩ B) = P(A)×P(B).
独立事件 – 一个事件发生与否不影响另一个事件的概率。P(A ∩ B) = P(A)×P(B)。
Memory tip: "Independent" means they do not depend on each other – they go their own way.
记忆窍门：“Independent” 表示它们互不依赖，各走各路。
5. Random Variables and Expectation | 随机变量与期望
Random variable (r.v.) – a variable whose value is a numerical outcome of a random phenomenon. Denoted by X, Y, etc.
随机变量 – 取值由随机现象决定的数值变量。用 X、Y 等表示。
Memory tip: It is "random" and it "varies" – hence random variable.
记忆窍门：它是“随机的”并且“变化的”，因此叫随机变量。
Discrete random variable – takes a countable number of distinct values. Probability distribution is given by a table or function p(x) = P(X=x).
离散随机变量 – 取值是可数个不同值。概率分布用表格或函数 p(x) = P(X=x) 给出。
Memory tip: "Discrete" means separate, distinct – you can count them one by one.
记忆窍门：“Discrete” 意为分开的、不连续的，可以一个一个数出来。
Continuous random variable – takes any value in an interval. Described by a probability density function (pdf) f(x). Probabilities are found by areas under the curve.
连续随机变量 – 可在某一区间内取任意值。用概率密度函数 (pdf) f(x) 描述，概率由曲线下面积给出。
Memory tip: "Continuous" means it flows without gaps, like water from a tap.
记忆窍门：“Continuous” 表示它无间断地流动，像水龙头流水。
Expectation (Expected value) E(X) – the mean of a random variable over repeated trials. For discrete, E(X) = Σ x·p(x). For continuous, E(X) = ∫ x·f(x) dx.
期望 (E(X)) – 随机变量在大量重复试验中的平均值。离散型：E(X) = Σ x·p(x)；连续型：E(X) = ∫ x·f(x) dx。
Memory tip: What you "expect" on average in the long run – the centre of gravity of the probability distribution.
记忆窍门：长期平均中你所“期待”的值，即概率分布的重心。
6. Common Distributions | 常见分布
Binomial distribution – X ~ B(n, p). Models the number of successes in n independent trials, each with probability p of success.
二项分布 – X ~ B(n, p)。模拟 n 次独立试验中成功的次数，每次成功概率为 p。
Memory tip: "Bi-" implies two outcomes (success/failure), "nomial" sounds like "number of trials".
记忆窍门：“Bi-” 表示两种结果（成功/失败），“nomial” 让人联想到试验次数。
Poisson distribution – X ~ Po(λ). Models the number of events occurring in a fixed interval of time or space, with mean rate λ.
泊松分布 – X ~ Po(λ)。模拟在固定时间或空间间隔内发生的事件数，平均发生率为 λ。
Memory tip: "Poisson" is French for "fish" – imagine counting fish caught per hour, a classic Poisson process!
记忆窍门：“Poisson” 在法语中是“鱼”，想象计算每小时钓到的鱼数，正是泊松过程的经典例子！
Normal distribution – X ~ N(μ, σ²). The bell-shaped curve, symmetric about μ, with inflection points at μ ± σ.
正态分布 – X ~ N(μ, σ²)。钟形曲线，关于 μ 对称，拐点在 μ ± σ。
Memory tip: "Normal" because it pops up "normally" in nature whenever many small independent effects add up.
记忆窍门：“Normal” 因为它经常在自然界中出现，当许多微小独立效应叠加时，它就会“正常”地出现。
7. Hypothesis Testing | 假设检验
Null hypothesis H₀ – the default statement being tested, usually “no effect” or “no difference”. Assumed true unless evidence suggests otherwise.
原假设 H₀ – 被检验的默认陈述，通常是“无效应”或“无差异”。除非有证据表明，否则假定为真。
Memory tip: "Null" means zero, nothing – H₀ is the hypothesis of "nothing happening".
记忆窍门：“Null” 意味着零、无 – H₀ 是“无事发生”的假设。
Alternative hypothesis H₁ (or HA) – the statement we accept if the null is rejected. It can be one-tailed (directional) or two-tailed.
备择假设 H₁ （或 HA） – 如果拒绝原假设则接受的陈述。可以是单尾（有方向）或双尾的。
Memory tip: "Alternative" is the other option – it’s what we’re really trying to prove.
记忆窍门：“Alternative” 是另一种选择，是我们真正想要证明的。
p-value – the probability, under H₀, of obtaining a result at least as extreme as the observed one. Small p-value → evidence against H₀.
p 值 – 在原假设为真的条件下，获得至少与实际观测一样极端的结果的概率。p 值越小，反对 H₀ 的证据越强。
Memory tip: "p" stands for "probability of being wrong if you reject H₀". The smaller, the better.
记忆窍门：“p” 代表“如果你拒绝 H₀ 就犯错的概率”。p 越小越好。
Significance level α – the threshold below which p-value is deemed significant; commonly 0.05 or 0.01. The tolerable risk of Type I error.
显著性水平 α – p 值低于此阈值则认为结果显著；常用 0.05 或 0.01。是允许犯第一类错误的风险上限。
Memory tip: α is the "action" level – when p falls below α, you take action and reject H₀.
记忆窍门：α 是“行动”水平 – 当 p 值低于 α，你就采取行动拒绝 H₀。
8. Errors in Testing | 检验中的错误
Type I error – rejecting H₀ when it is true. Probability = α.
第一类错误 – 原假设为真却拒绝它。概率为 α。
Memory tip: Type I is a "false alarm" – you see a fire where there is none. (α = alarm going off falsely)
记忆窍门：第一类错误是“虚惊一场” – 你看见了根本不存在的火。（α = 错误地拉响警报）
Type II error – failing to reject H₀ when H₁ is true. Probability = β.
第二类错误 – 备择假设为真却未能拒绝原假设。概率为 β。
Memory tip: Type II is a "missed detection" – a fire exists but you fail to spot it. (β = blind to the truth)
记忆窍门：第二类错误是“漏警” – 火灾发生，但你未能发现。（β = 对真相视而不见）
Power of a test = 1 − β, the probability of correctly rejecting H₀ when H₁ is true.
检验功效 = 1 − β，当备择假设为真时正确拒绝原假设的概率。
Memory tip: "Power" is the test’s ability to detect a real effect – stronger test, higher power.
记忆窍门：“Power” 是检验发现真实效应的能力 – 检验越强，功效越高。
9. Correlation and Regression | 相关与回归
Correlation coefficient r – measures the strength and direction of a linear relationship between two variables. −1 ≤ r ≤ 1.
相关系数 r – 衡量两个变量之间线性关系的强度和方向。−1 ≤ r ≤ 1。
Memory tip: "Co-relation" = how much they relate together. r near ±1 means strong co-relation.
记忆窍门：“Co-relation” = 它们关联的程度。r 接近 ±1 表示强关联。
Spearman’s rank correlation coefficient rs – based on ranks, used for monotonic relationships or ordinal data.
斯皮尔曼等级相关系数 rs – 基于排名的相关系数，用于单调关系或有序数据。
Memory tip: "Spearman" – think of a "spear" that ranks warriors in order of strength.
记忆窍门：“Spearman” – 想象一支长矛（spear）按实力给武士排名。
Regression line – the best-fit line ŷ = a + bx that minimises the sum of squared residuals. b is the slope, a the intercept.
回归直线 – 最佳拟合直线 ŷ = a + bx，使残差平方和最小。b 是斜率，a 是截距。
Memory tip: "Regression" means going back – the line estimates how y goes back (responds) to changes in x.
记忆窍门：“Regression” 意为回退 – 该直线估计 y 如何对 x 的变化做出“回归”。
Residual = observed y − predicted ŷ. It’s the vertical gap between a point and the regression line.
残差 = 观测值 y − 预测值 ŷ。它是数据点与回归直线之间的垂直差距。
Memory tip: "Residual" sounds like "residue" – the leftover part after fitting the line.
记忆窍门：“Residual” 像 “residue”（残留物），是直线拟合后剩余的部分。
10. Sampling and Bias | 抽样与偏差
Population – the entire group being studied. Sample – a subset selected from the population.
总体 – 被研究的整个群体。样本 – 从总体中选出的子集。
Memory tip: "Population" is the whole pie; "Sample" is a slice you taste to infer the whole.
记忆窍门：“Population” 是整个馅饼，“Sample” 是你尝的一片，用来推断整个。
Random sampling – every member has an equal chance of being chosen. Avoids bias.
随机抽样 – 每个成员被选中的机会相等。避免偏差。
Memory tip: "Random" originates from "randon," old French for "running fast" – no one can control who gets chosen.
记忆窍门：“Random” 源于古法语 “randon”（快速奔跑）– 没有人能控制谁被选中。
Bias – systematic error that causes results to differ from the true value. Arises from poor sampling or measurement.
偏差 – 引起结果偏离真值的系统性误差。源于抽样或测量过程不当。
Memory tip: "Bias" = "bi-" + "-as" – a one-sided influence that makes you lean in one direction.
记忆窍门：“Bias” 像 “bi-” 和 “-as”，一种单侧影响，让你倾向一边。
11. Data Representation Quick References | 数据展示速查
Histogram – a bar chart for continuous data where area is proportional to frequency. Frequency density = frequency ÷ class width.
直方图 – 用于连续数据的条形图，面积与频率成正比。频率密度 = 频率 ÷ 组距。
Memory tip: "Histo-" looks like "histogram" has "history" in it – but better think of it as grouping data into "stories" of intervals.
记忆窍门：“Histo-” 看起来像 “history”，但更好的联想是把数据按区间编成“故事”。
Box-and-whisker plot – displays quartiles, median, and potential outliers. Good for comparing distributions.
箱线图 – 显示四分位数、中位数和可能的异常值。适合比较分布。
Memory tip: The "box" captures the middle 50%; the "whiskers" stretch out to the extremes.
记忆窍门：“box” 容纳中间 50%， “whiskers” 向两头延伸。
Cumulative frequency curve – a graph showing the running total of frequencies. Use it to estimate medians and percentiles.
累积频率曲线 – 显示频率累计总和的图。用来估计中位数和百分位数。
Memory tip: "Cumulative" means "pile up". The curve keeps piling up heights as you go along.
记忆窍门：“Cumulative” 意为“堆积”。随着横轴增加，曲线不断向上堆积。
12. Quick Mnemonic Recap | 速记口诀总结
English: "Mean-Median-Mode / Range-IQR-SD / Null-Alpha-Pval / Errors-Power-Rank"
中文： “均值中位众数 // 极差四分位标准差 // 原假设显著性 p 值 // 两类错误功效排 // 分布二项泊松正 // 相关回归样偏差”
Use these rhythmic chunks to recall the vocabulary framework of WJEC Statistics.
用这些押韵的口诀来记住 WJEC 统计学的词汇框架。
Published by TutorHao | Statistics Revision Series | aleveler.com
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