📚 A-Level Edexcel Statistics: Essential Vocabulary Memorisation Guide | A-Level Edexcel 统计：词汇术语速记指南
Mastering statistical terminology is the first step towards excelling in Edexcel A-Level Statistics. This guide presents key terms in logical groups, with clear explanations and paired Chinese translations to help bilingual learners build confidence and accuracy.
掌握统计术语是在 Edexcel A-Level 统计学中取得优异成绩的第一步。本指南按逻辑分组呈现关键词汇，附有清晰的解释和中英对照，帮助双语学习者建立信心与准确度。
1. Types of Data | 数据类型
Qualitative data describes categories or qualities – for example, eye colour or blood type. It cannot be measured numerically but can be counted in frequency tables.
定性数据描述类别或属性，例如眼睛颜色或血型。它无法用数值测量，但可以在频数表中计数。
Quantitative data consists of numerical measurements. It is subdivided into discrete data (countable, like number of cars) and continuous data (measurable, like height or time).
定量数据由数值测量组成。它又分为离散数据（可数的，如汽车数量）和连续数据（可测量的，如身高或时间）。
2. Measures of Central Tendency | 集中趋势度量
The mean (x̄ for a sample, μ for a population) is the arithmetic average. It is sensitive to extreme values and is used when data are roughly symmetric.
均值（样本记为 x̄，总体记为 μ）是算术平均数。它对极端值敏感，适用于数据大致对称的情况。
The median is the middle value when data are ordered. It is robust to outliers and preferred for skewed distributions.
中位数是将数据排序后的中间值。它对异常值不敏感，适用于偏态分布。
The mode is the most frequently occurring value. A set may have one mode (unimodal), two modes (bimodal), or more.
众数是出现频率最高的值。数据集可以有一个众数（单峰）、两个众数（双峰）或更多。
3. Measures of Dispersion | 离散度量
Range = maximum value – minimum value. It gives a rough idea of spread but ignores the distribution shape.
极差 = 最大值 – 最小值。它给出数据分散程度的粗略概念，但忽略了分布形态。
Interquartile range (IQR) = Q₃ – Q₁. It covers the middle 50% of data and is resistant to outliers.
四分位距 (IQR) = Q₃ – Q₁。它涵盖了中间 50% 的数据，对异常值有抵抗力。
Variance (σ² for population, s² for sample) measures the average squared deviation from the mean. Standard deviation (σ or s) is the square root of variance and shares the same units as data.
方差（总体 σ²，样本 s²）衡量各数据与均值之差的平方的平均值。标准差（σ 或 s）是方差的平方根，与数据单位相同。
4. Probability Basics | 概率基础
An experiment is a repeatable process with uncertain outcomes. The sample space (S) is the set of all possible outcomes. An event is a subset of the sample space.
实验是一个可重复、结果不确定的过程。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。
The probability of an event A is denoted P(A). For equally likely outcomes, P(A) = number of favourable outcomes / total number of outcomes. Probability must satisfy 0 ≤ P(A) ≤ 1.
事件 A 的概率记为 P(A)。对于等可能结果，P(A) = 有利结果数 / 总结果数。概率必须满足 0 ≤ P(A) ≤ 1。
The complement of A, written A’, is the event that A does not occur; P(A’) = 1 – P(A).
A 的对立事件记为 A’，即 A 不发生的事件；P(A’) = 1 – P(A)。
5. Conditional Probability and Independence | 条件概率与独立性
Conditional probability P(B|A) means the probability of B occurring given that A has occurred. Formula: P(B|A) = P(A ∩ B) / P(A), provided P(A) > 0.
条件概率 P(B|A) 表示在事件 A 已经发生的条件下，事件 B 发生的概率。公式：P(B|A) = P(A ∩ B) / P(A)，其中 P(A) > 0。
Events A and B are independent if the occurrence of one does not affect the probability of the other. Mathematically, P(A ∩ B) = P(A) × P(B), or equivalently P(B|A) = P(B).
事件 A 与 B 相互独立，如果一个事件的发生不影响另一个事件发生的概率。数学上，P(A ∩ B) = P(A) × P(B)，或等价地 P(B|A) = P(B)。
Mutually exclusive events cannot occur at the same time; P(A ∩ B) = 0. This is different from independence.
互斥事件不可能同时发生；P(A ∩ B) = 0。这与独立性不同。
6. Random Variables and Distributions | 随机变量与分布
A random variable X assigns a numerical value to each outcome. It can be discrete (countable values) or continuous (any value within an interval).
随机变量 X 为每个结果分配一个数值。它可以是离散的（可数值）或连续的（区间内任意值）。
The probability distribution of a discrete X lists values and probabilities, with ∑ P(X = x) = 1. The expected value E(X) is the long-run average: E(X) = Σ x·P(X = x). Variance Var(X) = E(X²) – [E(X)]².
离散随机变量 X 的概率分布列出各值及其概率，且 ∑ P(X = x) = 1。期望值 E(X) 是长期平均值：E(X) = Σ x·P(X = x)。方差 Var(X) = E(X²) – [E(X)]²。
The binomial distribution B(n, p) models the number of successes in n independent trials with constant probability p. Its mean is np, variance np(1 – p).
二项分布 B(n, p) 模拟在 n 次独立试验中成功次数的分布，每次成功概率 p 不变。其均值为 np，方差为 np(1 – p)。
The normal distribution N(μ, σ²) is a continuous bell-shaped curve. About 68% of values lie within μ ± σ, 95% within μ ± 2σ, and 99.7% within μ ± 3σ. The standard normal Z ~ N(0, 1²) is used for probability calculations via z = (x – μ)/σ.
正态分布 N(μ, σ²) 是连续的钟形曲线。约 68% 的值落在 μ ± σ 范围内，95% 在 μ ± 2σ，99.7% 在 μ ± 3σ。标准正态分布 Z ~ N(0, 1²) 用于概率计算，通过 z = (x – μ)/σ 转换。
7. Sampling Methods | 抽样方法
A population is the entire set of items under study; a sample is a subset selected for investigation. A sampling frame is a list of all population members.
总体是研究对象的全体集合；样本是为调查而选出的子集。抽样框是总体所有成员的列表。
Simple random sampling gives every member an equal chance of selection, avoiding bias. Stratified sampling divides the population into groups (strata) and samples proportionally from each.
简单随机抽样让每个成员有相等的被选机会，避免偏差。分层抽样将总体分成若干层，并按比例从各层抽样。
Systematic sampling selects every k-th element from a list. Cluster sampling selects entire groups naturally formed. Quota sampling is non-probability, selecting predetermined numbers reflecting population characteristics.
系统抽样从列表中每隔 k 个抽取一个元素。整群抽样选取自然形成的整个群组。配额抽样是非概率抽样，按预定数量选取以反映总体特征。
8. Hypothesis Testing | 假设检验
The null hypothesis H₀ is a statement of no effect or no difference, assumed true until evidence suggests otherwise. The alternative hypothesis H₁ states what we suspect or hope to prove.
零假设 H₀ 是一个“无效应或差异”的陈述，在证据充分前被视为成立。备择假设 H₁ 是我们怀疑或想要证明的陈述。
A test statistic measures how far the observed sample result deviates from H₀. The p-value is the probability of obtaining a result at least as extreme as observed, assuming H₀ is true.
检验统计量衡量观测样本结果与 H₀ 之间的偏差程度。p 值是在 H₀ 为真的前提下，得到至少与观测结果同样极端的概率。
Significance level α (commonly 0.05) is the threshold for rejecting H₀. If p-value ≤ α, result is statistically significant; reject H₀. Type I error is rejecting a true H₀; Type II error is failing to reject a false H₀.
显著性水平 α（通常为 0.05）是拒绝 H₀ 的门槛。若 p 值 ≤ α，结果统计显著，拒绝 H₀。第一类错误是拒绝了一个真实的 H₀；第二类错误是未能拒绝一个错误的 H₀。
9. Correlation and Regression | 相关与回归
The product moment correlation coefficient r (Pearson’s r) measures the strength and direction of a linear relationship between two variables. –1 ≤ r ≤ 1; values near ±1 indicate strong linear correlation, near 0 weak.
积矩相关系数 r（皮尔逊 r）衡量两个变量之间线性关系的强度和方向。–1 ≤ r ≤ 1；接近 ±1 表示强线性相关，接近 0 表示弱相关。
The regression line of y on x is y = a + bx, where b = Sxy / Sxx and a = ȳ – b x̄. Sxy = Σ(x – x̄)(y – ȳ), Sxx = Σ(x – x̄)².
y 对 x 的回归直线为 y = a + bx，其中 b = Sxy / Sxx，a = ȳ – b x̄。Sxy = Σ(x – x̄)(y – ȳ)，Sxx = Σ(x – x̄)²。
Interpolation (predicting within the range of data) is reliable; extrapolation (outside the range) can be misleading. Residuals are the differences between observed y and predicted y.
内插（在数据范围内预测）是可靠的；外推（超出范围）可能产生误导。残差是观测 y 值与预测 y 值之间的差值。
10. Quick Symbol Reference | 常用符号速记
| Symbol | Meaning | 中文解释 |
| x̄ | Sample mean | 样本均值 |
| μ | Population mean | 总体均值 |
| σ | Population standard deviation | 总体标准差 |
| s | Sample standard deviation | 样本标准差 |
| σ² | Population variance | 总体方差 |
| Σ | Sum | 求和 |
| P(A) | Probability of event A | 事件 A 的概率 |
| ∩ | Intersection (and) | 交集（且） |
| ∪ | Union (or) | 并集（或） |
| P(B|A) | Conditional probability | 条件概率 |
| X ~ N(μ, σ²) | X follows a normal distribution | X 服从正态分布 |
| X ~ B(n, p) | X follows a binomial distribution | X 服从二项分布 |
Familiarity with these symbols and terms will speed up problem-solving and reduce confusion during exams. Practise reading the notation aloud every time you encounter it.
熟悉这些符号和术语可以加快解题速度，减少考试中的困惑。每次遇到时，都出声读一读这些记号。
11. Data Representation Vocabulary | 数据呈现术语
Histogram: a graphical display for continuous data where area of bars represents frequency. Frequency density = frequency / class width. Unlike a bar chart, bars touch.
直方图：连续数据的图形显示，条形面积代表频数。频数密度 = 频数 / 组距。与条形图不同，条形之间没有间隔。
Box plot (box-and-whisker plot) displays minimum, Q₁, median, Q₃, and maximum, and can identify outliers defined as values below Q₁ – 1.5×IQR or above Q₃ + 1.5×IQR.
箱形图（盒须图）显示最小值、Q₁、中位数、Q₃ 和最大值，并能识别异常值，异常值定义为小于 Q₁ – 1.5×IQR 或大于 Q₃ + 1.5×IQR 的数值。
Cumulative frequency curve (ogive) plots cumulative frequencies against upper class boundaries and is used to estimate medians and percentiles.
累积频数曲线（拱形图）以累积频数对上组界绘制，用于估计中位数和百分位数。
12. Key Phrases in Hypothesis Tests | 假设检验关键短语
‘Assume H₀ is true’ is the starting model. ‘Test statistic’ (z, t, or binomial probability) is calculated. ‘Critical region’ is the set of values for which H₀ is rejected.
“假设 H₀ 为真”是起点模型。计算“检验统计量”（z、t 或二项概率）。“拒绝域”是使 H₀ 被拒绝的数值集合。
‘p-value < significance level' leads to rejecting H₀. Interpret the conclusion in context: 'There is sufficient evidence to suggest that...' or 'There is insufficient evidence...'.
“p 值 < 显著性水平”导致拒绝 H₀。在上下文中解释结论：“有充分证据表明……”或“没有充分证据……”。
Always link conclusion back to the original claim. Never say ‘accept H₀’; say ‘do not reject H₀’ because absence of evidence is not evidence of absence.
始终将结论与原始声明联系起来。永远不要说“接受 H₀”，应说“不拒绝 H₀”，因为证据不足不等于证明其真。
Published by TutorHao | Statistics Revision Series | aleveler.com
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