📚 A-Level Eduqas Statistics: Key Vocabulary Quick Memorisation Guide | A-Level Eduqas 统计：词汇术语速记指南
Mastering the precise terminology of Statistics is the first step to excelling in the Eduqas A-Level examination. This guide breaks down the essential vocabulary into logical themes, pairing each definition with its Chinese equivalent for rapid reinforcement. Use it as a daily drill or a last-minute checklist to ensure you never confuse a parameter with a statistic, or Type I with Type II error.
掌握精确的统计术语是你在Eduqas A-Level考试中脱颖而出的第一步。这份指南将核心词汇按主题分组，并进行中英配对解释，便于快速记忆。把它当作每日训练或考前最后的检查表，确保你决不会混淆参数与统计量，或是第Ⅰ类错误与第Ⅱ类错误。
1. Population and Sample | 总体与样本
A population is the complete set of individuals, items, or data under investigation. Every member of the population is of interest in a statistical enquiry.
总体是被调查的全部个体、项目或数据构成的完整集合。统计研究中关注的是总体的每一个成员。
A sample is a subset of the population selected for study. It is used to draw conclusions about the population without examining every member.
样本是从总体中选出的一个子集，用于代表总体进行研究，从而无需逐个调查即可推断总体的特征。
A census is an attempt to measure or observe every member of a population. While it eliminates sampling error, it is often costly and time-consuming.
普查是对总体中每一个成员进行测量或观察的尝试。虽然它消除了抽样误差，但通常成本高昂且耗时。
A sampling unit is an individual element from the population that is available for selection at some stage of the sampling process. A sampling frame is a list of all sampling units from which the sample is drawn.
抽样单位是总体中可以用于抽样的单个元素。抽样框架则是包含所有抽样单位的名册，样本即从中抽取。
A parameter is a numerical characteristic of a population, such as the population mean μ or population variance σ². It is usually unknown and estimated from sample data.
参数是描述总体特征的数值，如总体均值 μ 或总体方差 σ²。它通常是未知的，需要通过样本数据进行估计。
A statistic is a numerical characteristic calculated from a sample, for example the sample mean x̄ or sample standard deviation s. It serves as an estimator of the corresponding population parameter.
统计量是从样本计算出的数值特征，例如样本均值 x̄ 或样本标准差 s。它用来估计相应的总体参数。
2. Types of Data and Variables | 数据类型与变量
Qualitative (categorical) data are non-numerical observations, such as hair colour, blood type, or satisfaction rating. They may be nominal (no natural order) or ordinal (ordered categories).
定性（分类）数据是非数字的观察结果，例如发色、血型或满意度评分。它们可以是名义的（无自然顺序）或定序的（有顺序类别）。
Quantitative data are numerical observations that can be further classified as discrete or continuous. Discrete data arise from counting and can only take certain values (e.g. number of goals). Continuous data arise from measuring and can take any value within a range (e.g. height, time).
定量数据是数值型的观察结果，可进一步分为离散型和连续型。离散数据来自计数，只能取某些特定值（如进球数）。连续数据来自测量，可以在一个区间内取任意值（如身高、时间）。
An explanatory (independent) variable is the one that is manipulated or used to predict changes in a response variable. In a regression context, it is often plotted on the x-axis.
解释（自）变量是被操控或用来预测响应变量变化的变量。在回归中，它通常绘制在 x 轴上。
A response (dependent) variable is the outcome that is measured and is expected to change in response to the explanatory variable. It is usually plotted on the y-axis.
响应（因）变量是测量的结果，预期会随解释变量的改变而改变。它通常绘制在 y 轴上。
Bivariate data consist of paired observations of two variables from the same individuals. They are fundamental for studying correlation and regression.
双变量数据由来自同一个体的两个变量的成对观察值组成，是研究相关与回归的基础。
3. Measures of Central Tendency | 集中趋势度量
The arithmetic mean of a data set is the sum of all values divided by the number of observations. For a population it is denoted μ; for a sample x̄.
x̄ = Σx / n
数据集的算术平均值是所有数值之和除以观测值个数。总体均值用 μ 表示，样本均值用 x̄ 表示。
The median is the middle value when the data are arranged in ascending order. It is less affected by outliers than the mean and is often used with skewed distributions.
中位数是将数据按升序排列后位于中间的值。它受极端值的影响比均值小，常用于偏态分布。
The mode is the value that occurs most frequently in a data set. A data set can have more than one mode (bimodal or multimodal) or no mode at all.
众数是数据集中出现频率最高的值。一个数据集可能有多个众数（双众数或多众数），也可能没有众数。
The weighted mean assigns different weights to each value, reflecting its relative importance. It is calculated as the sum of each value multiplied by its weight, divided by the sum of the weights.
加权均值根据相对重要性为每个值分配不同的权重。计算方法为各值乘以其权重后求和，再除以权重总和。
4. Measures of Dispersion | 离散程度度量
The range is the simplest measure of dispersion, defined as the difference between the largest and smallest values in the data set.
极差是最简单的离散度量，定义为数据集中最大值与最小值之差。
The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁). It measures the spread of the middle 50% of the data and is resistant to outliers.
四分位距（IQR）是上四分位数（Q₃）与下四分位数（Q₁）之差。它衡量中间 50% 数据的散布情况，且不受极端值影响。
Variance measures the average squared deviation from the mean. The population variance is σ², while the sample variance is s²:
s2 = Σ(x − x̄)2 / (n − 1)
方差衡量数据相对于均值的平均平方偏差。总体方差为 σ²，样本方差为 s²，公式如上（分母用 n−1 以给出无偏估计）。
The standard deviation is the positive square root of the variance and has the same units as the original data. It is denoted σ for a population and s for a sample.
标准差是方差的正平方根，与原数据单位相同。总体标准差写作 σ，样本标准差写作 s。
A common rule identifies an outlier as any value below Q₁ − 1.5×IQR or above Q₃ + 1.5×IQR.
异常值是指与其他数值距离异常远的观测点。常见判定法则是：小于 Q₁ − 1.5×IQR 或大于 Q₃ + 1.5×IQR 的值被视为异常值。
5. Probability Basics and Random Variables | 概率基础与随机变量
An experiment is a repeatable process that gives rise to a number of possible outcomes. The set of all possible outcomes is called the sample space.
试验是一个可重复的过程，会产生多个可能的结果。所有可能结果的集合称为样本空间。
ent A, P(A), satisfies 0 ≤ P(A) ≤ 1, with P(sample space) = 1 and P(impossible event) = 0.
事件是样本空间的子集。事件 A 的概率 P(A) 满足 0 ≤ P(A) ≤ 1，其中样本空间的概率为 1，不可能事件的概率为 0。
A random variable is a variable whose value depends on the outcome of a random experiment. It can be discrete (countable values) or continuous (any value in an interval).
随机变量是其取值依赖于随机试验结果的变量。它可以是离散的（可数个值）或连续的（某区间内的任意值）。
A probability distribution lists all possible values of a discrete random variable together with their probabilities, which sum to 1.
概率分布列出一个离散随机变量的所有可能取值及其对应的概率，所有概率之和为 1。
discrete random variable X is E(X) = Σx·P(X=x). The variance is Var(X) = E(X²) − [E(X)]².
离散随机变量 X 的期望值（均值）为 E(X) = Σx·P(X=x)。方差为 Var(X) = E(X²) − [E(X)]²。
6. Discrete Probability Distributions (Binomial & Poisson) | 离散概率分布（二项与泊松）
The binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success p. We write X ~ B(n, p).
二项分布描述在固定次数独立试验中成功的次数，每次试验成功概率相同 p。记作 X ~ B(n, p)。
The probability mass function of a binomial random variable is:
P(X = r) = nCr pr (1 − p)n−r
二项随机变量的概率质量函数如上。其均值 E(X) = np，方差 Var(X) = np(1−p)。
A binomial distribution is appropriate when the number of trials n is fixed, each trial is independent, there are only two outcomes (success/failure), and the probability of success p remains constant.
适用二项分布的条件为：试验次数 n 固定，各次试验独立，每次只有两种结果（成功/失败），且成功概率 p 保持不变。
The Poisson distribution models the number of events occurring in a fixed interval of time or space, given a known average rate λ. It is used for rare events. We write X ~ Po(λ).
泊松分布用于模拟固定时间或空间区间内随机事件发生的次数，已知平均发生率 λ。适用于稀有事件。记作 X ~ Po(λ)。
The probability mass function of a Poisson random variable is:
P(X = r) = e−λ λr / r!
泊松随机变量的概率质量函数如上。其均值和方差均等于 λ，即 E(X) = Var(X) = λ。
7. The Normal Distribution | 正态分布
The normal distribution is a continuous probability distribution with a bell-shaped probability density curve. It is fully defined by its mean μ and standard deviation σ; we write X ~ N(μ, σ²).
正态分布是一种连续型概率分布，其概率密度曲线呈钟形。它完全由均值 μ 和标准差 σ 决定，记作 X ~ N(μ, σ²)。
The standard normal distribution has a mean of 0 and standard deviation of 1: Z ~ N(0, 1). Any normal variable can be standardised using:
Z = (X − μ) / σ
标准正态分布的均值为 0，标准差为 1，记作 Z ~ N(0,
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