📚 AQA Year 12 Statistics: Key Terms & Vocabulary Quick Revision Guide | AQA 12 年级统计：关键术语与词汇速记指南
Building a strong statistics vocabulary is half the battle in AQA Year 12. This guide pairs every key term with a memorable hook and a clear Chinese explanation, helping you move from confusion to confidence quickly.
在 AQA 12 年级统计中，扎实的词汇基础是成功的一半。本指南将每个关键术语与易记口诀及清晰的中文解释配对，帮你快速摆脱困惑，树立信心。
1. Population, Sample, Parameter & Statistic | 总体、样本、参数与统计量
A population is the entire set of individuals or items we want to study. A sample om the population. Remember the P-P and S-S trick: Population → Parameter (both start with 'P'), Sample → Statistic (both start with 'S').
总体是我们想研究的全部个体或项目的集合。样本是从总体中抽取的一个较小子集。记住 P-P 和 S-S 口诀：总体 (Population) 对应参数 (Parameter)，都以 P 开头；样本 (Sample) 对应统计量 (Statistic)，都以 S 开头。
A parameter is a numerical summary describing a population (e.g., the true population mean μ). A statistic is a numerical summary calculated from a sample (e.g., the sample mean x̄). Sample statistics are used to estimate population parameters.
参数是描述总体的数字概括（例如真实的总体均值 μ）。统计量是从样本计算出的数字概括（例如样本均值 x̄）。样本统计量用于估计总体参数。
The sampling frame is a list of all members of the population from which the sample is drawn. Each element in the frame is a sampling unit. A good sampling frame should be complete and up-to-date.
抽样框是总体所有成员的列表，样本从中抽取。框中的每个元素就是一个抽样单元。一个好的抽样框应当完整且及时更新。
2. Types of Data: Qualitative vs Quantitative, Discrete vs Continuous | 数据类型：定性/定量，离散/连续
Qualitative data bing qualities or categories (e.g., hair colour, car brand). Think: Quality = descriptive. Quantitative data re are numerical, measuring quantities (e.g., height, temperature). Think: Quantity = numbers.
定性数据是非数值的，描述性质或类别（例如发色、汽车品牌）。联想：质量 (Quality) 是描述性的。定量数据是数值型的，测量数量（例如身高、温度）。联想：数量 (Quantity) 与数字相关。
Quantitative data split further into discrete and continuous . Discrete data can only take specific, separate values, usually whole numbers (e.g., number of goals scored). Remember 'discrete = distinct, counting'. Continuous data can take any value within a range (e.g., weight, time). Remember 'continuous = continuum, measuring'.
定量数据进一步分为离散和连续。离散数据只能取特定的、分离的值，通常是整数（例如进球数）。记住“离散 = 可数、分开”。连续数据可以在一个区间内取任意值（例如体重、时间）。记住“连续 = 连绵不断、测量”。
Within qualitative data we also meet ordinal and nominal. Nominal data are labels with no natural order (e.g., eye colour). Ordinal data have a natural order but unequal gaps between ranks (e.g., satisfaction ratings: poor, fair, good). Think: Ordinal – Order.
在定性数据内部我们还会遇到有序和无序。无序（名义）数据是仅作标签，无自然顺序（例如眼睛颜色）。有序数据有自然顺序，但等级间间距不等（例如满意度评级：差、一般、好）。联想：有序 — 有顺序。
3. Sampling Methods: From Random to Quota | 抽样方法：从随机到配额
Simple random sampling gives every member of the population an equal chance of being selected. This can be done by lottery or random number tables. It removes bias but requires a complete sampling frame.
简单随机抽样赋予总体中每个成员相等的被选中的机会。可通过抽签或随机数表实现。它消除偏差，但需要一个完整的抽样框。
Stratified sampling divides the population into distinct groups (strata) based on a characteristic, then takes a random sample from each stratum proportional to size. It ensures representation of all groups.
分层抽样按某一特征将总体划分为不同的组（层），然后从每层中按比例抽取随机样本。它保证了所有组的代表性。
Systematic sampling selects every k-th item from the sampling frame. Start randomly, then take every k-th. Easy to use, but can introduce hidden patterns.
系统抽样从抽样框中每隔 k 个抽取一个。随机起点，然后每隔 k 个选取。使用简便，但可能引入隐藏模式。
Quota sampling is a non-probability method where the interviewer selects a predetermined number of people from categories. It does not require a sampling frame and is cheap, but suffers from interviewer bias.
配额抽样是一种非概率方法，采访者按事先确定的类别人数选择对象。不需抽样框，成本低，但存在采访者偏差。
Opportunity (convenience) sampling uses whoever is available at the time. It is quick and easy but rarely representative. Remember: opportunists grab what's handy!
便利（机会）抽样利用当时恰好可用的个体。快捷易行，但极少具有代表性。记住：投机者捡现成的！
4. Measures of Central Tendency: Mean, Median & Mode | 集中趋势度量：均值、中位数、众数
Mean (x̄) number of values. It uses every piece of data, making it sensitive to outliers. Formula: x̄ = Σx / n. Think: mean = average, pulls toward extreme values.
均值 (x̄)：所有数据值之和除以数据个数。它利用了每一个数据，因而对异常值敏感。公式：x̄ = Σx / n。联想：均值即平均数，会被极端值拉走。
Median: the middle value when data are ordered. It splits the data into two equal halves. For n data points: position is (n+1)/2. The median is resistant to outliers – it stays put when extremes appear.
中位数：数据排序后位于中间的值。它将数据平分为两半。数据个数 n 的位置：(n+1)/2。中位数耐抗异常值——极端值出现时它稳如磐石。
Mode : the most frequently occurring value. There can be no mode, one mode (unimodal) or multiple modes. Useful for categorical data. Memory: Mode = Most often.
众数：出现频率最高的值。可以没有众数、单众数或多众数。对分类数据尤其有用。记忆：众 = 最多。
5. Measures of Spread: Range, IQR, Variance & Standard Deviation | 离散程度：极差、四分位距、方差、标准差
Range = maximum – measure of spread but only uses two extreme values, so it is highly affected by outliers.
极差 = 最大值 – 最小值。它是最简单的离散度量，但只用了两个极端值，极容易受异常值影响。
Interquartile range (IQR) = Q₃ – Q₁, the middle 50% the upper quartile (median of upper half). IQR eliminates the influence of extreme values.
四分位距 (IQR) = Q₃ – Q₁，即数据的中间50%。Q₁ 是下四分位数（下半部分的中位数），Q₃ 是上四分位数（上半部分的中位数）。IQR 排除了极端值的影响。
Variance (σ² or s²): average squared deviation from the mean. Population Var = Σ(x – μ)² / N; Sample Var = Σ(x – x̄)² / (n – 1). The units are squared, which can be hard to interpret.
方差 (σ² 或 s²)：各数据与均值之差的平方的平均数。总体方差 = Σ(x – μ)² / N；样本方差 = Σ(x – x̄)² / (n – 1)。其单位是平方，解释起来不太直观。
Standard deviation (σ or s) d is the most commonly used measure of spread. Think: SD = typical distance from the mean.
标准差 (σ 或 s)：方差的平方根。它与原始数据单位相同，是最常用的离散度量。联想：标准差 = 数据点到均值的典型距离。
An outlier × IQR below Q₁ or above Q₃. Outliers may be due to measurement error or natural variation.
异常值可定义为比 Q₁ 低 1.5×IQR 以上或比 Q₃ 高 1.5×IQR 以上的数值。异常值可能源于测量误差或自然变异。
6. Probability Terminology: Events, Independence & Conditional Probability | 概率术语：事件、独立性、条件概率
An experiment is a repeatable process that gives outcomes. The sample space (S) is the set of all possible outcomes. An event mple space. Probability of event A: P(A) = number of favourable outcomes / total outcomes.
试验是一个可重复并产生结果的过程。样本空间 (S) 是所有可能结果的集合。事件是样本空间的子集。事件 A 的概率：P(A) = 有利结果数 / 总结果数。
Mutually exclusive events cannot occur at the same time. P(A ∩ B) = 0 and P(A ∪ B) = P(A) + P(B). Memory: Mutually exclusive = mutually excluding.
互斥事件不能同时发生。P(A ∩ B) = 0，且 P(A ∪ B) = P(A) + P(B)。记忆：互斥 = 互相排斥。
Independent events have no influence on each other's probabilities. P(A ∩ B) = P(A) × P(B). Check independence by seeing if P(A|B) = P(A). Memory: independent = no influence.
独立事件相互之间不影响概率。P(A ∩ B) = P(A) × P(B)。可通过检验 P(A|B) = P(A) 来确认独立性。记忆：独立 = 互不影响。
Conditional probability P(A|B) is the probability of A given that B has occurred. Formula: P(A|B) = P(A ∩ B) / P(B). Always reduce the sample space to event B. Think: given = restricted world.
条件概率 P(A|B) 是在 B 已发生的条件下 A 发生的概率。公式：P(A|B) = P(A ∩ B) / P(B)。始终将样本空间缩减至事件 B。联想：给定条件 = 缩小后的世界。
7. Discrete Random Variables: Expectation & Variance | 离散随机变量：期望与方差
A discrete random variable =x) = 1. A probability distribution describes all possible values and their probabilities.
离散随机变量 (X) 取一组可数的值，每个值都有对应的概率。所有概率之和必须为 1：ΣP(X=x) = 1。概率分布描述所有可能的取值及其概率。
Expectation E(X) average if the experiment is repeated many times. Memory: Expectation = expected average.
期望 E(X) 是分布的理论均值。E(X) = Σ x·P(X=x)。它表示若试验重复多次的长期平均值。记忆：期望 = 预期的平均。
Variance Var(X) measures the spread of the distribution. Var(X) = E(X²) – E(X)]², where E(X²) = Σ x²·P(X=x). This formula is much quicker than computing deviations.
方差 Var(X) 衡量分布的离散程度。Var(X) = E(X²) – [E(X)]²，其中 E(X²) = Σ x²·P(X=x)。该公式比计算偏差平方要快得多。
8. Binomial Distribution: Conditions, Notation & Moments | 二项分布：条件、符号与矩
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success p. Conditions: fixed number of trials n, each trial has two outcomes (success/failure), trials are independent, and p is constant.
二项分布用于描述在固定次数的独立试验中成功次数的分布，每次试验成功概率 p 相同。条件：试验次数 n 固定，每次试验只有两种结果（成功/失败），各次试验独立，p 保持不变。
Notation: X ~ B(n, p). The probability of exactly r successes: P(X = r) = ⁿCᵣ pʳ (1 – p)ⁿ⁻ʳ. Use calculator or tables. Memory: Binomial = Bi (two outcomes) + nomial (count number).
符号：X ~ B(n, p)。恰好有 r 次成功的概率：P(X = r) = ⁿCᵣ pʳ (1 – p)ⁿ⁻ʳ。使用计算器或查表。记忆：二项 = 两种结果 + 计数。
Mean and variance: E(X) = np, Var(X) = np(1 – p). The variance is maximum when p = 0.5. These formulas are easy to recall: mean = 'number × probability'.
均值与方差：E(X) = np，Var(X) = np(1 – p)。当 p = 0.5 时方差最大。这些公式容易记忆：均值 = 次数 × 概率。
9. Normal Distribution: Properties, Standardisation & Z-values | 正态分布：性质、标准化与Z值
The normal distribution is a continuous bell-shaped curve defined by mean μ and standard deviation σ. Notation: X ~ N(μ, σ²). It is symmetric about μ, and total area under the curve = 1. About 68% of data lie within μ ± σ; 95% within μ ± 2σ.
正态分布是一条连续钟形曲线，由均值 μ 和标准差 σ 定义。符号：X ~ N(μ, σ²)。它关于 μ 对称，曲线下总面积为 1。大约 68% 的数据落在 μ ± σ 内，95% 落在 μ ± 2σ 内。
Standard normal distribution Z ~ N(0, 1²) has mean 0 and standard deviation 1. To standardise any normal variable X, use:
Z = (X – μ) / σ
标准正态分布 Z ~ N(0, 1²) 均值为 0，标准差为 1。对任何正态变量 X 进行标准化，用：Z = (X – μ) / σ。
The Z-value tells you how many standard deviations X is from the mean. Memory: Z is the 'z-distance' measured in σ-units. Use Z-tables or inverse normal to find probabilities and percentiles.
Z 值告诉你 X 距离均值多少个标准差。记忆：Z 就是以 σ 为单位测量的“标准距离”。使用 Z 表或逆正态求概率和百分位数。
10. Correlation & Regression: Strength, Direction & Prediction | 相关与回归：强度、方向与预测
Correlation measures the strength and direction of a linear relationship between two variables. A scatter diagram shows paired data (x, y). Look for pattern, direction (positive/negative) and strength.
相关衡量两个变量之间线性关系的强度和方向。散点图展示成对数据 (x, y)。观察形态、方向（正/负）以及强度。
Product moment correlation coefficient (PMCC) tion; r = -1: perfect negative; r = 0: no linear correlation. Use calculator to compute r.
积矩相关系数 (PMCC)，记为 r，是一个介于 -1 和 +1 之间的数值。r = 1：完全正线性相关；r = -1：完全负线性相关；r = 0：无线性相关。用计算器求 r。
Regression line ummarises the linear relationship and makes predictions. Equation: y = a + bx, where b = Sxy / Sxx and a = ȳ – b x̄. The line always passes through (x̄, ȳ).
回归线（最小二乘法）概括线性关系并进行预测。方程：y = a + bx，其中 b = Sxy / Sxx，a = ȳ – b x̄。该直线始终经过点 (x̄, ȳ)。
Important: correlation does not imply causation. Beware of extrapolation – predicting outside the range of the data can be unreliable.
重要：相关并不意味因果关系。警惕外推——超出数据范围的预测是不可靠的。
11. Hypothesis Testing: Steps, Significance & Errors | 假设检验：步骤、显著性及错误
Hypothesis testing is a formal procedure to decide whether evidence supports a claim. You start with a null hypothesis H₀ (status quo, no change) and an alternative hypothesis H₁ (what you suspect). For binomial tests on p, H₀: p = p₀, H₁: p < p₀, p > p₀ or p ≠ p₀.
假设检验是一个正式程序，用于判断证据是否支持某个主张。从原假设 H₀（现状，无变化）和备择假设 H₁（你所怀疑的）开始。对于 p 的二项检验，H₀: p = p₀，H₁ 可为 p < p₀，p > p₀ 或 p ≠ p₀。
The test statistic is the observed number of successes from the sample. The significance level (α) is the maximum probability of rejecting H₀ when it is true. Common α is 5% (0.05).
检验统计量是样本观测到的成功次数。显著性水平 (α) 是当 H₀ 为真时拒绝 H₀ 的最大概率。常用 α = 5% (0.05)。
The critical region (rejection region) contains values for which H₀ is rejected. It is found using binomial distribution assuming H₀ is true. The p-value sult at least as extreme as the observed one, given H₀ is true. If p-value ≤ α, reject H₀.
临界域（拒绝域）包含导致拒绝 H₀ 的统计量值。它在假设 H₀ 为真的条件下用二项分布求得。p 值是在 H₀ 为真的条件下，获得至少与观测值同样极端的结果的概率。若 p 值 ≤ α，则拒绝 H₀。
Two types of error: Type I error – rejecting H₀ when it is true (probability = α). Type II error – it is false (probability = β). Memory: Type I = false positive, Type II = false negative.
两种错误：第一类错误—— H₀ 为真却被拒绝（概率 = α）。第二类错误—— H₀ 为假却没有被拒绝（概率 = β）。记忆：第一类 = 假阳性，第二类 = 假阴性。
12. Data Representation: Box Plots, Histograms & Cumulative Frequency | 数据呈现：箱线图、直方图与累积频率
A box plot (box-and-whisker) displays minimum, Q₁, median, Q₃ and maximum. It visualises spread, skewness and identifies outliers. The box covers IQR; whiskers extend to the furthest non-outlier points.
箱线图（盒须图）显示最小值、Q₁、中位数、Q₃ 和最大值。它能直观呈现离散程度、偏态和识别异常值。盒体覆盖 IQR；须延伸至最远的非异常值点。
Histograms ght = frequency density = frequency / class width. No gaps between bars. Memory: Histogram – Height linked to density.
直方图用于连续数据，每个条块的面积代表频数。条块高度 = 频率密度 = 频数 / 组距。条块之间无间隙。记忆：直方图 – 高度与密度挂钩。
Cumulative frequency is the running total of frequencies. A cumulative frequency curve (ogive) plots upper class boundary against cumulative frequency. Use it to estimate medians, quartiles and percentiles. The median is found at 50% of total frequency.
累积频率是频数的累加和。累积频率曲线（折线图）以上组界为横坐标，累积频率为纵坐标绘制。用于估计中位数、四分位数和百分位数。中位数位于总频率的 50% 处。
Also, a frequency polygon al, joins midpoints of each class interval, useful for comparing distributions. Remember: polygon = points linked like a necklace.
另外，频率多边形连接每个组区间的中点，便于比较分布。记忆：多边形 = 像项链一样串起的点。
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