📚 Year 12 CIE Statistics: Vocabulary & Terminology Quick Memorisation Guide | Year 12 CIE 统计：词汇术语速记指南
Mastering the vocabulary of statistics is half the battle in Year 12 CIE exams. This guide breaks down essential terms topic by topic, pairing precise English definitions with clear Chinese translations, and includes memory aids to help you quickly recall each concept under exam pressure.
攻克 Year 12 CIE 统计考试，词汇术语是半壁江山。本指南按主题拆解核心术语，将准确的英文定义与清晰的中文翻译配对，并融入记忆技巧，帮助你在考试压力下快速调用每个概念。
1. Data Types & Graphical Representation | 数据类型与图表展示
Qualitative data: non‑numerical information that describes qualities or categories (e.g. eye colour, car brand). It is often displayed using bar charts or pie charts.
定性数据：描述性质或类别的非数值信息（如眼睛颜色、汽车品牌），常用条形图或饼图展示。
Quantitative data: numerical information that can be measured or counted. It is divided into discrete (integer counts) and continuous (any value on a scale).
定量数据：可以测量或计数的数值信息，分为离散型（整数计数）和连续型（标尺上任意取值）。
Discrete variable: a quantitative variable that takes only separate, distinct values, usually integers (e.g. number of students). Think "countable gaps".
离散变量：仅取分离、可辨识值的定量变量，通常为整数（如学生人数）。记法：可数的间隔。
Continuous variable: a quantitative variable that can take any value in an interval (e.g. height, time). Its graphs use histograms or frequency polygons.
连续变量：在一个区间内可取任意值的定量变量（如身高、时间），其图表使用直方图或频数多边形。
Frequency distribution: a table or graph that shows how often each value or class occurs. Grouped frequency combines data into intervals (classes).
频数分布：展示每个数值或组出现次数的表格或图形。分组频数将数据合并为区间（组）。
Histogram: a diagram for grouped continuous data where area of each bar is proportional to frequency. Unlike a bar chart, bars touch and width matters.
直方图：分组连续数据的图示，每块面积与频数成比例。与条形图不同，柱体相连且宽度重要。
Cumulative frequency graph (ogive): a line graph that plots the running total of frequencies against the upper boundary of each class. Use it to estimate medians and quartiles.
累积频数图（Ogive）：将频数的累计和与每组上限对应绘制的折线图，用于估算中位数和四分位数。
Box‑and‑whisker plot (box plot): a visual representation of the five-number summary: minimum, lower quartile (Q₁), median (Q₂), upper quartile (Q₃), maximum. It highlights outliers and symmetry.
箱线图：用五数概括（最小值、下四分位数Q₁、中位数Q₂、上四分位数Q₃、最大值）直观展示数据，突出异常值及对称性。
Outlier well outside the main pattern, often defined as more than 1.5 × IQR below Q₁ or above Q₃.
异常值：远离主要模式的数值，通常以低于 Q₁ – 1.5×IQR 或高于 Q₃ + 1.5×IQR 为标准。
2. Measures of Central Tendency | 集中趋势度量
Mean (arithmetic mean) bservations divided by the number of observations. Highly affected by outliers. Formula: x̄ = Σx/n.
算术平均数：所有观测值之和除以观测个数，极易受异常值影响。公式：x̄ = Σx/n。
Median : the middle value when data are ordered. For n values, position = (n+1)/2. It is resistant to outliers – a "robust" measure.
中位数：排序后居中的数值，位置 = (n+1)/2。不受异常值影响，是“稳健”的度量。
Mode: the value that occurs most frequently. A data set can have one mode (unimodal), two (bimodal), or none.
众数：出现次数最多的值。数据集可为单峰（单众数）、双峰（双众数）或无众数。
Weighted mean: an average where each value is assigned a weight reflecting its importance. Used when combining means from different groups.
加权平均数：每个数值按重要性赋予权重后计算的平均值，用于合并来自不同组别的均值。
Skewness: a measure of asymmetry. In a positively skewed distribution, mean > median > mode; in a negatively skewed one, mean < median < mode.
偏度：不对称性的度量。正偏态分布中，均值 > 中位数 > 众数；负偏态则相反。
3. Measures of Spread | 离散度量
Range: maximum – minimum. Quick but sensitive to outliers.
极差：最大值减最小值，计算快但对异常值敏感。
Interquartile range (IQR): Q₃ – Q₁. Covers the middle 50% of data; resilient against outliers.
四分位距 (IQR)：第三四分位数减第一四分位数，覆盖中间50%的数据，抗异常值能力强。
Variance (σ² for population, s² for sample): the average of squared deviations from the mean. Formula for a set of values: s² = Σ(x – x̄)²/(n–1) or using Σx²/n – x̄².
方差（总体 σ²，样本 s²）：各数值与均值之差的平方的平均数。公式：s² = Σ(x – x̄)²/(n–1)，或使用 Σx²/n – x̄²。
Standard deviation (σ or s): the square root of variance; returned to the original unit, measuring typical deviation from the mean.
标准差（σ 或 s）：方差的平方根，回到原始单位，衡量与均值的典型偏离程度。
Mean deviation (mean absolute deviation): average of absolute deviations from the mean. Less common in CIE but useful for conceptual understanding.
平均差：各值与均值之差的绝对值的平均数，CIE中使用较少，但有助理解概念。
Percentile: the value below which a given percentage of observations fall. For example, the 90th percentile is higher than 90% of data.
百分位数：给定百分比的观测值落在其下方的值，如第90百分位数高于90%的数据。
4. Probability Fundamentals | 概率基础
Random experiment: a process that leads to one of several possible outcomes, with inherent unpredictability (e.g. rolling a die).
随机试验：产生若干个可能结果之一的过程，且结果具有内在不可预测性（如掷骰子）。
Sample space (S): the set of all possible outcomes of an experiment. For a coin toss, S = {H, T}.
样本空间 (S)：试验所有可能结果的集合，如抛硬币 S = {正面, 反面}。
Event (A, B, …): a subset of the sample space; something we can assign a probability to.
事件：样本空间的子集，我们可以为之分配概率。
Probability of A, P(A) ) = number of favourable outcomes / total number of outcomes, for equally likely outcomes.
概率 P(A)：0到1之间的数，度量事件A发生的可能性；等可能结果下 P(A) = 有利结果数 / 总结果数。
Mutually exclusive events: events that cannot happen at the same time; P(A ∩ B) = 0. Addition rule simplifies to P(A ∪ B) = P(A) + P(B).
互斥事件：不能同时发生的事件，P(A ∩ B) = 0。加法规则简化为 P(A ∪ B) = P(A) + P(B)。
Independent events: occurrence of one does not affect the probability of the other; P(A ∩ B) = P(A) × P(B). Do not confuse with mutually exclusive!
独立事件：一个事件的发生不影响另一个事件的概率，P(A ∩ B) = P(A) × P(B)。切勿与互斥混淆！
Conditional probability, P(A|B): probability of A given that B has occurred; P(A|B) = P(A ∩ B) / P(B). Tree diagrams can help.
条件概率 P(A|B)：在B已发生的条件下A发生的概率；P(A|B) = P(A ∩ B) / P(B)。树图可助理解。
Addition rule: P(A ∪ B) = P(A) + P(B) – P(A ∩ B). Subtract overlap to avoid double‑counting.
加法法则：P(A ∪ B) = P(A) + P(B) – P(A ∩ B)。减去重叠部分以防重复计算。
Complement rule: P(A') = 1 – P(A). A' means “not A”. Very handy for “at least one” problems.
补集法则：P(A') = 1 – P(A)。A' 表示“非A”。处理“至少一个”类问题时极为方便。
5. Counting: Permutations & Combinations | 计数：排列与组合
Factorial (n!): n! = n × (n–1) × … × 2 × 1, with 0! = 1. It counts the number of ways to arrange n distinct objects in order.
阶乘 (n!)：n! = n × (n–1) × … × 2 × 1，且 0! = 1，用于计算n个不同物体的排列方式总数。
Permutation (ⁿPᵣ or nPr) to arrange r objects chosen from n distinct objects, where order matters. Formula: nPr = n!/(n–r)!.
排列 (ⁿPᵣ)：从n个不同物体中选出r个并按顺序排列的方式数。公式：nPr = n!/(n–r)!。
Combination (ⁿCᵣ or nCr) to choose r objects from n distinct objects, where order does NOT matter. Formula: nCr = n!/[r!(n–r)!].
组合 (ⁿCᵣ)：从n个不同物体中无序选出r个的方式数。公式：nCr = n!/[r!(n–r)!]。
Distinguishing arrangements with repeated items: total arrangements = n! / (a! b! …), where a, b are frequencies of identical items.
重复元素的排列：当存在相同物品时，总排列数 = n! / (a! b! …)，a, b 为各类相同元素的个数。
Multiplication principle ways, the combined task can be done in m×n ways. Underpins permutations and combinations.
乘法原理：若任务A有m种完成方法，任务B有n种，则两任务先后完成共有 m×n 种方法。这是排列组合的基础。
6. Discrete Random Variables | 离散随机变量
Random variable (X) of a random experiment; denoted by capital letters, e.g. X = number of heads in 3 tosses.
随机变量 (X)：取值依赖于随机试验结果的变量，用大写字母表示，如 X = 掷3次硬币出现正面的次数。
Probability distribution of X: a table, graph, or formula listing all possible values of X and their probabilities. All probabilities sum to 1.
X的概率分布：列出X所有可能取值及其概率的表格、图表或公式，概率总和为1。
Expected value E(X) or μ: the long‑run average value of X; E(X) = Σ [x · P(X = x)]. It is a weighted mean, the “centre” of the distribution.
期望值 E(X) 或 μ：X 的长期平均值；E(X) = Σ [x · P(X = x)]。它是以概率为权重的加权平均值，即分布的“中心”。
Variance Var(X) or σ²: measure of spread; Var(X) = E[(X–μ)²] = E(X²) – [E(X)]². The second form is faster for calculation.
方差 Var(X) 或 σ²：离散程度量度；Var(X) = E[(X–μ)²] = E(X²) – [E(X)]²。第二式计算更便捷。
Linear transformation of X Var(aX + b) = a² Var(X). Adding a constant shifts the mean but does not change the spread.
X 的线性变换：E(aX+b) = a E(X) + b，Var(aX+b) = a² Var(X)。加常数仅平移均值，不改变离散程度。
Cumulative distribution function F(x) crete variables it is a step function; useful for finding probabilities of ranges quickly.
累积分布函数 F(x)：F(x) = P(X ≤ x)。对离散变量它是阶梯函数，便于快速计算区间概率。
7. Binomial Distribution | 二项分布
Binomial conditions: a fixed number n of independent trials, each trial has only two possible outcomes (success/failure), probability of success p is constant. Mnemonic: "BINS" – Binary outcome, Independent, Number fixed, Same p.
二项分布条件：固定次数 n 的独立试验，每次试验只有两种可能结果（成功/失败），成功概率 p 恒定。助记：“BINS” – 二元结果 (Binary)、独立 (Independent)、次数固定 (Number fixed)、同概率 (Same p)。
Probability mass function: P(X = k) = ⁿCₖ pᵏ (1 – p)ⁿ⁻ᵏ, for k = 0, 1, …, n. The term (1–p) is often written as q.
概率质量函数：P(X = k) = ⁿCₖ pᵏ (1 – p)ⁿ⁻ᵏ, k = 0,1,…,n。常记 1–p 为 q。
Mean and variance: For X ~ B(n, p), E(X) = np, Var(X) = npq. Remember: “mean = n × p, variance = mean × q”.
均值和方差：若 X ~ B(n, p)，则 E(X) = np, Var(X) = npq。记住：“均值 = n × p，方差 = 均值 × q”。
Shape of the distribution n p = 0.5, positively skewed when p < 0.5, negatively skewed when p > 0.5, for moderate n.
分布形状：当 p = 0.5 时对称；p < 0.5 时正偏；p > 0.5 时负偏（对于中等 n 值）。
Using tables for cumulative probabilities ide binomial cumulative tables. Use them to find P(X ≤ k), then derive P(X = k) = P(X ≤ k) – P(X ≤ k–1).
查表求累积概率：CIE考试提供二项累积表。先查得 P(X ≤ k)，再通过 P(X = k) = P(X ≤ k) – P(X ≤ k–1) 求单点概率。
Binomial as a sample proportion: If X ~ B(n, p), then the proportion of successes is p̂ = X/n, with E(p̂) = p, Var(p̂) = pq/n. This lays the ground for sampling distributions.
二项分布与样本比例：若 X ~ B(n, p)，则成功比例 p̂ = X/n，期望为 p，方差为 pq/n，为抽样分布打基础。
8. Normal Distribution | 正态分布
Continuous bell‑shaped curve: the normal distribution is defined by two parameters: mean μ and variance σ². It is symmetric about μ, and the total area under the curve is 1.
连续钟形曲线：正态分布由两个参数定义：均值 μ 和方差 σ²。关于 μ 对称，曲线下总面积为1。
Standard normal Z ~ N(0, 1): a normal variable transformed by Z = (X – This gives Z a mean of 0 and standard deviation of 1, allowing the use of a single table.
标准正态 Z ~ N(0,1)：通过 Z = (X – μ)/σ 将正态变量标准化，使 Z 均值为0、标准差为1，从而可使用唯一一张概率表。
Using the standard normal table: the table gives P(Z < z), i.e. the cumulative probability up to z. For other intervals, use symmetry and complement rules.
标准正态表的使用：表格提供 P(Z < z)，即 Z 累积概率。其他区间可借助对称性和补集法则处理。
Empirical rule (68–95–99.7 rule): about 68% of data fall within μ ± σ, 95% within μ ± 2σ, 99.7% within μ ± 3σ. Useful for quick checks.
经验法则（68–95–99.7规则）：约68%数据落在 μ ± σ，95%在 μ ± 2σ，99.7%在 μ ± 3σ。适合快速检核。
Inverse normal: given a probability (area to the left), find the corresponding z‑value, then un‑standardise: x = μ + zσ. Make sure the probability matches the table direction.
逆正态：已知概率（左侧面积），求出对应 z 值，再反标准化：x = μ + zσ。注意确保概率方向与表格一致。
Continuity correction (for normal approximation to binomial): when using normal to approximate binomial, replace P(X = k) with P(k–0.5 < X < k+0.5) for better accuracy.
连续性校正：用正态近似二项时，将 P(X = k) 换成 P(k–0.5 < X < k+0.5) 以提高精确度。（此概念在 Year 12 后期可能涉及）
9. Sampling & Estimation | 抽样与估计
Population vs. Sample: population is the whole group we want to study; a sample is a subset selected to represent it. Good sampling is random and unbiased.
总体与样本：总体是我们想研究的全组对象；样本是从中选出的子集。好的抽样应随机且无偏。
Random sample: every member of the population has an equal chance of being selected. This ensures the sample's representativeness.
随机样本：总体中每个成员被选中的机会均等，以此保证样本代表性。
Statistic: a numerical quantity calculated from a sample (e.g. sample mean x̄, sample proportion p̂). It is used to estimate the corresponding population parameter.
统计量：由样本计算得出的数值（如样本均值 x̄
Published by TutorHao | Year 12 统计 Revision Series | aleveler.com
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