📚 Year 13 AQA Statistics: Vocabulary and Terminology Quick Reference Guide | AQA统计学词汇术语速记指南
Mastering the precise vocabulary of statistics is essential for success in Year 13 AQA Statistics. Marks are frequently lost not because the mathematics is difficult, but because a definition is vague, a hypothesis is worded carelessly, or a term such as 'independent' is confused with 'mutually exclusive'. This quick reference guide pairs every key term with a concise definition and, where relevant, the formula or exam convention that goes with it, so that you can move confidently through sampling, probability, distributions, correlation and inference.
掌握精确的统计词汇是 AQA 统计学 Year 13 取得成功的关键。很多失分并非因为数学太难，而是因为定义写得含糊、假设表述不严谨，或者把 'independent'（独立）与 'mutually exclusive'（互斥）混为一谈。本速记指南把每个关键术语与简洁定义配对，并在需要时附上相应的公式或考试规范，帮助你自信地应对抽样、概率、分布、相关与统计推断。
1. Basic Statistical Vocabulary | 基本统计词汇
Population: the entire collection of individuals, items or data values that are the subject of a study.
总体：研究中全部个体、项目或数据值的集合。
Sample: a subset of the population, selected so that it can represent the whole and provide estimates about its characteristics.
样本：总体的一个子集，被选取以代表总体并提供关于总体特征的估计。
Parameter: a numerical summary that describes a characteristic of a population, for example the population mean μ or the population proportion p. Parameters are usually unknown and are denoted by Greek letters.
参数：描述总体某特征的数值概括，例如总体均值 μ、总体比例 p。参数通常未知，用希腊字母表示。
Statistic: a numerical summary calculated from a sample, used to estimate a population parameter, for example the sample mean x̄ or the sample proportion p̂. Statistics are denoted by Roman letters and vary from sample to sample.
统计量：从样本计算出的数值概括，用于估计总体参数，例如样本均值 x̄、样本比例 p̂。统计量用拉丁字母表示，并随样本而变化。
Census: a study that collects data from every member of the population. It removes sampling error but is usually slower, more expensive and sometimes impossible.
普查：从总体的每个成员收集数据的研究。普查可消除抽样误差，但通常更慢、更贵，有时甚至无法实施。
Variable: any characteristic that can take different values for different individuals, such as height, test score or eye colour.
变量：对不同个体可以取不同值的任何特征，例如身高、考试成绩或眼睛颜色。
Data value (observation): a single recorded measurement or response belonging to one individual or item.
数据值（观测值）：属于某一个体或项目的单次记录测量值或回答。
Sample size: the number of individuals or items in the sample, usually written n. A larger n generally reduces the variability of a statistic.
样本容量：样本中个体或项目的数量，通常记作 n。n 越大，统计量的变异性通常越小。
A quick reminder of the standard notation used throughout the course:
课程中通用的标准记号速查：
| Symbol | Meaning / 含义 |
| μ, σ, p | Population mean, standard deviation, proportion / 总体均值、标准差、比例 |
| x̄, s, p̂ | Sample mean, standard deviation, proportion / 样本均值、标准差、比例 |
| n | Sample size / 样本容量 |
| N | Population size / 总体容量 |
| Σ | Sum of the following values / 对后续所有值求和 |
2. Sampling Methods and Sampling Frames | 抽样方法与抽样框
Sampling frame: a list of all the members of the population from which a sample is drawn, such as a register of students or a list of postcodes. If the frame is incomplete, the sample is biased.
抽样框：总体所有成员的名单，样本由此抽取，例如学生名册或邮编列表。如果抽样框不完整，样本就会有偏。
Simple random sampling: every member of the population has an equal chance of being selected, and every sample of size n is equally likely. Random number generators or lottery methods are used.
简单随机抽样：总体中每个成员被选中的机会均等，且每个容量为 n 的样本被抽中的可能性相同。通常使用随机数生成器或抽签法。
Systematic sampling: members are selected at regular intervals from an ordered list, for example every 10th name after a random start. Beware of periodic patterns in the list.
系统抽样：从有序名单中按固定间隔抽取成员，例如随机起点后每隔 10 个取一个。要警惕名单中存在的周期性规律。
Stratified sampling: the population is divided into strata that share a characteristic (for example year group or gender), and a random sample is taken from each stratum in proportion to its size.
分层抽样：将总体按某一特征划分为若干层（例如年级或性别），然后在每层中按该层规模的比例进行随机抽样。
Cluster sampling: the population is divided into clusters (for example schools or streets), a random selection of clusters is chosen, and every member within the chosen clusters is surveyed.
整群抽样：将总体划分为若干群（例如学校或街道），随机抽取若干群，并对被抽中群内的每个成员进行调查。
Quota sampling: the interviewer fills fixed quotas of individuals with certain characteristics. It is quick but not random, so it cannot be used for reliable inference.
配额抽样：访问员按预先设定的特征配额寻找受访者。该方法快捷但非随机，因此不能用于可靠的统计推断。
Opportunity (convenience) sampling: whoever is available at the time is used, for example the first 50 people in a shopping centre.
机会抽样（便利抽样）：只使用当时可得的人，例如购物中心里最先遇到的 50 个人。
Bias: a systematic tendency for a sample or estimate to differ from the truth in one direction, caused by a flawed sampling method rather than by chance.
偏差：样本或估计值系统性偏向某一方向而偏离真值的倾向，其成因是抽样方法有缺陷，而非偶然因素。
Non-response: the failure of selected individuals to provide data. High non-response can introduce bias if non-responders differ systematically from responders.
无应答：被选中个体未能提供数据。若无应答者与应答者存在系统性差异，高无应答率会引入偏差。
Sampling variability: the natural variation between the values of a statistic from one sample to another. It decreases as the sample size increases.
抽样变异性：不同样本所得统计量数值之间的自然差异。样本容量越大，抽样变异性越小。
3. Types of Data and Variables | 数据类型与变量
Qualitative (categorical) data: data that describe qualities or categories rather than amounts, such as favourite colour or qualification type.
定性（分类）数据：描述性质或类别而非数量的数据，例如最喜欢的颜色或资格证书类型。
Nominal data: categorical data with no natural order, for example modes of transport.
名义数据：没有自然顺序的分类数据，例如出行方式。
Ordinal data: categorical data with a meaningful order but unequal or undefined gaps, for example a satisfaction scale from 'poor' to 'excellent'.
有序数据：具有有意义顺序、但间隔不等或未定义的分类数据，例如从 'poor' 到 'excellent' 的满意度量表。
Quantitative (numerical) data: data that record amounts or counts and can be used in calculations.
定量（数值）数据：记录数量或计数的数据，可用于计算。
Discrete data: numerical data that take only particular values, usually counts such as the number of defective items or the number of goals.
离散数据：只能取特定值的数值数据，通常是计数，例如次品数或进球数。
Continuous data: numerical data that can take any value within a range, such as time, mass or temperature, limited only by the precision of measurement.
连续数据：在某一范围内可取任意值的数值数据，例如时间、质量或温度，仅受测量精度限制。
Explanatory variable: the variable that is thought to explain or predict changes in another variable. It is plotted on the horizontal axis.
解释变量：被认为能解释或预测另一变量变化的变量，绘制在横轴上。
Response variable: the variable being predicted or explained. It is plotted on the vertical axis.
响应变量：被预测或被解释的变量，绘制在纵轴上。
Grouped data: continuous or discrete data collected into intervals. For grouped data we use the midpoint of each class interval to estimate means and totals.
分组数据：按区间收集的连续或离散数据。对分组数据，我们使用每个组区间的组中值来估计均值与总量。
Outlier t of the distribution, commonly defined as more than 1.5 × IQR beyond the nearer quartile.
异常值：远离其余分布的不寻常数据值，通常定义为超出邻近四分位数 1.5 × IQR 之外的值。
4. Probability Vocabulary | 概率词汇
Experiment (trial): a repeatable process with an uncertain outcome, such as rolling a die or selecting a card.
试验：结果不确定的可重复过程，例如掷骰子或抽一张牌。
Outcome: a single possible result of an experiment.
结果：试验的某一个可能结局。
Sample space (S): the set of all possible outcomes, written S or ξ.
样本空间（S）：所有可能结果的集合，记作 S 或 ξ。
Event: a collection of one or more outcomes, that is, a subset of the sample space.
事件：一个或多个结果的集合，即样本空间的一个子集。
Complement: the event that A does not occur, written A′. P(A′) = 1 − P(A).
补事件：A 不发生的事件，记作 A′。P(A′) = 1 − P(A)。
Mutually exclusive events: events that cannot occur at the same time, so P(A ∩ B) = 0.
互斥事件：不可能同时发生的事件，因此 P(A ∩ B) = 0。
Independent events: events where the occurrence of one does not affect the probability of the other, so P(A ∩ B) = P(A) × P(B) and P(A | B) = P(A).
独立事件：一个事件的发生不影响另一个事件发生的概率，因此 P(A ∩ B) = P(A) × P(B) 且 P(A | B) = P(A)。
Conditional probability: the probability that A occurs given that B has occurred.
条件概率：在 B 已发生的条件下 A 发生的概率。
P(A ∪ B) = P(A) + P(B) − P(A ∩ B)
P(A | B) = P(A ∩ B) ÷ P(B), P(B) ≠ 0
For mutually exclusive events the addition rule simplifies to P(A ∪ B) = P(A) + P(B), while for independent events the multiplication rule gives P(A ∩ ns are not independent, so conditional probabilities must be recalculated after each draw.
对于互斥事件，加法法则简化为 P(A ∪ B) = P(A) + P(B)；对于独立事件，乘法法则给出 P(A ∩ B) = P(A) × P(B)。当抽取是不放回时，连续两次抽取并不独立，因此每次抽取后都必须重新计算条件概率。
5. Random Variables, Expectation and Variance | 随机变量、期望与方差
Random variable: a variable whose value depends on the outcome of a random experiment. It is usually denoted by a capital letter such as X.
随机变量：取值取决于随机试验结果的变量，通常用大写字母表示，如 X。
Discrete random variable: a random variable that can take only distinct, separate values, such as 0, 1, 2, 3.
离散随机变量：只能取互不相同的分立值的随机变量，例如 0、1、2、3。
Continuous random variable s probability distribution is described by a curve, and P(X = x) = 0 for any single value.
连续随机变量：可在某一区间内取任意值的随机变量，其概率分布由曲线描述，且对任何单个值都有 P(X = x) = 0。
Probability distribution andom variable together with their probabilities. For a discrete variable, Σ P(X = x) = 1.
概率分布：对随机变量所有可能取值及其相应概率的完整描述。对离散变量，Σ P(X = x) = 1。
Expected value (mean): the long-run average value of a random variable.
期望值（均值）：随机变量的长期平均值。
E(X) = Σ x P(X = x)
Var(X) = E(X²) − [E(X)]²
σ = √Var(X)
Variance: a measure of the spread of a distribution, defined as the expected value of the squared deviation from the mean. Its square root is the standard deviation.
方差：衡量分布离散程度的量，定义为偏离均值的平方的期望值，其平方根即标准差。
Coding and linear transformation constant does not change the spread, and multiplying by a negative a does not make the variance negative.
编码与线性变换：若 Y = aX + b，则 E(Y) = aE(X) + b，Var(Y) = a² Var(X)。注意，加上一个常数不改变离散程度，而乘以负数 a 也不会使方差变成负值。
ar(X ± Y) = Var(X) + Var(Y). Variances always add, even when the variables are subtracted.
对于相互独立的随机变量 X 与 Y：E(X ± Y) = E(X) ± E(Y)，且 Var(X ± Y) = Var(X) + Var(Y)。无论相加还是相减，方差始终相加。
6. The Binomial Distribution | 二项分布
Binomial distribution: the probability distribution of the number of successes in n independent trials, each with the same probability of success p.
二项分布：在 n 次独立试验中成功次数的概率分布，每次试验成功的概率均为 p。
The model applies when four conditions hold: there is a fixed number of trials n; each trial has exactly two outcomes, conventionally 'success' and 'failure'; the probability of success p is constant for every trial; and the trials are independent of one another.
该模型成立需满足四个条件：试验次数 n 固定；每次试验只有两种结果，通常称为 '成功' 与 '失败'；每次试验成功的概率 p 保持不变；各次试验相互独立。
Notation: we write X ~ B(n, p), read as 'X is distributed binomially with parameters n and p'.
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