📚 Year 13 Edexcel Statistics: Key Vocabulary & Terminology Quick Guide | Year 13 Edexcel 统计：词汇术语速记指南
Mastering Year 13 Edexcel Statistics isn’t just about crunching numbers — it’s about speaking the language of data with precision. This guide breaks down the most important terms you’ll meet in regression, probability, hypothesis testing, and more, pairing clear English definitions with memorable Chinese explanations to help you ace your exam.
掌握Year 13 Edexcel 统计不仅在于计算数字，更在于精准地使用数据的语言。本指南梳理了回归、概率、假设检验等模块中最重要的术语，用清晰的英文定义搭配易记的中文解释，助你在考试中脱颖而出。
1. Regression & Correlation | 回归与相关
The product moment correlation coefficient (PMCC), denoted r, measures the strength and direction of a linear relationship between two variables. It always lies between –1 and 1; a value close to 1 indicates strong positive correlation, while a value close to –1 indicates strong negative correlation.
积矩相关系数 (PMCC) 记作 r，衡量两个变量之间线性关系的强度和方向。它的值始终在 –1 到 1 之间；接近 1 表示强正相关，接近 –1 表示强负相关。
The least squares regression line is of the form y = a + bx, where b is the slope calculated from Sxy / Sxx. Its key property is that it minimises the sum of the squares of the vertical distances (residuals) from the data points to the line.
最小二乘回归线 形如 y = a + bx，其中斜率 b 由 Sxy / Sxx 算出。它的关键性质是使得数据点到直线的垂直距离（残差）的平方和最小。
A residual is the difference between an observed y-value and the value predicted by the regression line, calculated as y – ŷ. Patterns in residual plots can reveal non-linearity or heteroscedasticity.
残差 是观测的 y 值与回归线预测值之差，计算为 y – ŷ。残差图中的模式可以揭示非线性关系或异方差性。
2. Probability Distributions | 概率分布
A probability distribution describes how probabilities are spread over the possible values of a random variable. For discrete variables, P(X = x) gives the probability of exactly x; for continuous variables, we use a probability density function (PDF).
概率分布 描述概率在随机变量可能取值上的分布方式。对于离散变量，P(X = x) 给出恰好取值 x 的概率；对于连续变量，则使用概率密度函数 (PDF)。
The cumulative distribution function (CDF), F(x) = P(X ≤ x), accumulates probabilities up to a point. In a continuous distribution, the probability of any exact value is zero, so we work with intervals.
累积分布函数 (CDF) 记作 F(x) = P(X ≤ x)，将概率累积到某一点。在连续分布中，任何精确值的概率为零，因此我们处理的是区间概率。
Expectation or expected value E(X) is the long-run average taken over all possible outcomes, weighted by their probabilities. For a function g(X), E(g(X)) = Σ g(x)P(X=x).
期望 或称期望值 E(X) 是所有可能结果按其概率加权的长期平均值。对于函数 g(X)，E(g(X)) = Σ g(x)P(X=x)。
3. Normal Distribution | 正态分布
The normal distribution N(μ, σ²) is a bell-shaped continuous distribution defined by its mean μ and variance σ². The total area under the curve is 1, and the curve is symmetric around μ.
正态分布 N(μ, σ²) 是由均值 μ 和方差 σ² 定义的钟形连续分布。曲线下的总面积为 1，且关于 μ 对称。
The standard normal distribution Z ~ N(0, 1²) has mean 0 and standard deviation 1. Any normal variable X ~ N(μ, σ²) can be standardised using Z = (X – μ) / σ.
标准正态分布 Z ~ N(0, 1²) 的均值为 0，标准差为 1。任何正态变量 X ~ N(μ, σ²) 都可通过 Z = (X – μ) / σ 进行标准化。
The inverse normal function is used to find the value x for a given cumulative probability. This is essential for calculating confidence intervals and critical values in tests.
逆正态 函数用于在给定累积概率时求出对应的 x 值。这在计算置信区间和检验临界值时至关重要。
4. Binomial & Poisson Distributions | 二项分布与泊松分布
The binomial distribution X ~ B(n, p) models the number of successes in n independent trials, each with success probability p. Probability mass function: P(X = r) = ⁿCr pr (1 – p)n–r.
二项分布 X ~ B(n, p) 模拟 n 次独立试验中成功的次数，每次成功概率为 p。概率质量函数为 P(X = r) = ⁿCr pr (1 – p)n–r。
The Poisson distribution X ~ Po(λ) models the number of events occurring in a fixed interval of time or space, where λ is the average rate. Its mean and variance are both equal to λ.
泊松分布 X ~ Po(λ) 模拟在固定时间或空间区间内事件发生的次数，λ 是平均发生率。它的均值和方差都等于 λ。
When n is large and p is small, the binomial distribution can be approximated by a Poisson distribution with λ = np. This simplifies calculations when dealing with rare events.
当 n 很大且 p 很小时，二项分布可用泊松分布近似，其中 λ = np。这在处理稀有事件时能简化计算。
5. Hypothesis Testing Framework | 假设检验框架
A null hypothesis H₀ is a statement of no effect or no difference, assumed true until evidence suggests otherwise. The alternative hypothesis H₁ challenges H₀ and can be one-tailed or two-tailed.
原假设 H₀ 是关于无效应或无差异的陈述，在证据表明确凿之前假定为真。备择假设 H₁ 对 H₀ 提出质疑，可以是单尾或双尾的。
The significance level α (commonly 0.05) is the probability of rejecting H₀ when it is actually true — a Type I error. A p-value is the probability of obtaining a result at least as extreme as the observed one, assuming H₀ is true.
显著性水平 α（通常取 0.05）是当 H₀ 实际为真却拒绝它的概率——第一类错误。p值 是在假定 H₀ 为真的情况下，得到至少与观测结果一样极端的结果的概率。
A critical region (or rejection region) contains values of the test statistic that lead to rejecting H₀. The boundary of this region is the critical value obtained from the sampling distribution.
临界域（或拒绝域）包含导致拒绝 H₀ 的检验统计量的取值。该区域的边界是从抽样分布中得出的 临界值。
6. Sampling Methods & Bias | 抽样方法与偏差
A simple random sample gives every member of the population an equal chance of being selected. It reduces bias but can be impractical with large populations.
简单随机抽样 使总体中每个成员被选中的概率相等。它可以减少偏差，但在总体很大时不切实际。
Stratified sampling divides the population into distinct strata (e.g., age groups) and samples proportionally from each. This ensures representation of all key subgroups.
分层抽样 把总体分成不同的层（如年龄组），然后按比例从每层中抽样。这能确保所有关键子群都有代表性。
Sampling bias occurs when the sample does not accurately represent the population, often due to selection bias or non-response. Recognising bias is essential for drawing valid conclusions.
抽样偏差 指样本不能准确代表总体，常由选择偏差或无应答导致。识别偏差是得出有效结论的关键。
7. Estimation & Confidence Intervals | 估计与置信区间
A point estimate is a single value obtained from a sample to estimate a population parameter, such as the sample mean x̄ estimating μ. An interval estimate provides a range of plausible values.
点估计 是从样本中获得的一个单一值，用于估计总体参数，例如用样本均值 x̄ 估计 μ。区间估计 提供一组合理的取值范围。
A confidence interval for a mean is typically constructed as x̄ ± z* × (σ/√n) when σ is known, where z* is the critical value from the standard normal distribution. The confidence level (e.g., 95%) indicates the long-run proportion of such intervals that would contain the true parameter.
均值的 置信区间 在 σ 已知时通常构建为 x̄ ± z* × (σ/√n)，其中 z* 是标准正态分布的临界值。置信水平（如 95%）表示长期来看此类区间包含真实参数的比例。
8. Chi-Squared Tests | 卡方检验
A chi-squared test for goodness of fit determines whether observed frequencies match a hypothesized distribution. The test statistic χ² = Σ (O – E)² / E follows a χ²-distribution with degrees of freedom ν = number of categories – 1 (minus number of estimated parameters).
拟合优度卡方检验 用于判断观测频数是否与假设的分布相符。检验统计量 χ² = Σ (O – E)² / E 服从自由度为类别数 – 1（减去估计参数个数）的 χ² 分布。
A chi-squared test for association (or independence) examines whether two categorical variables are related in a contingency table. Degrees of freedom are (rows – 1) × (columns – 1). Cells with expected values below 5 may require combining categories.
独立性卡方检验 用于考察列联表中两个分类变量是否相关。自由度为（行数 – 1）×（列数 – 1）。如果单元格的期望值低于 5，可能需要合并类别。
9. Conditional Probability & Bayes’ Theorem | 条件概率与贝叶斯定理
Conditional probability P(A|B) is the probability of event A occurring given that B has occurred, defined as P(A ∩ B) / P(B). Tree diagrams and Venn diagrams are powerful tools for visualising these relationships.
条件概率 P(A|B) 是在事件 B 已发生的条件下事件 A 发生的概率，定义为 P(A ∩ B) / P(B)。树形图和文氏图是可视化这些关系的有力工具。
Bayes’ theorem links conditional probabilities: P(A|B) = [P(B|A) × P(A)] / P(B). It is used to update the probability of an event as new information becomes available — a cornerstone of statistical inference.
贝叶斯定理 连接条件概率：P(A|B) = [P(B|A) × P(A)] / P(B)。它用于在新信息出现时更新事件概率，是统计推断的基石。
10. Continuous Random Variables & PDF | 连续随机变量与概率密度函数
A probability density function (PDF) f(x) for a continuous random variable must satisfy f(x) ≥ 0 for all x, and the total area under the curve ∫ f(x) dx = 1. Probability is calculated by integrating the PDF over an interval.
连续随机变量的 概率密度函数 (PDF) f(x) 必须满足对所有 x 有 f(x) ≥ 0，且曲线下的总面积 ∫ f(x) dx = 1。概率通过在一个区间上对 PDF 积分来计算。
The median m of a continuous distribution is the value such that P(X ≤ m) = 0.5, found by solving ∫–∞m f(x) dx = 0.5. The mode is the value where f(x) attains its maximum.
连续分布的 中位数 m 是满足 P(X ≤ m) = 0.5 的值，通过解 ∫–∞m f(x) dx = 0.5 得到。众数 是 f(x) 取得最大值的点。
11. Large Data Set & Technology | 大数据集与技术
In Edexcel Statistics, you will work with a large data set (LDS) covering real weather data. Knowing the variables, units, and potential outliers helps you answer questions about sampling, summary statistics, and interpretations without full access to the data.
在 Edexcel 统计中，你将接触包含真实天气数据的 大数据集 (LDS)。熟悉其中的变量、单位和潜在异常值，有助于在无法查阅完整数据的情况下回答关于抽样、汇总统计和解释的问题。
Using technology such as calculators or spreadsheets to compute PMCC, regression coefficients, and distribution probabilities is expected. Understanding the output and being able to verify its reasonableness is crucial.
使用计算器或电子表格等 技术工具 来计算 PMCC、回归系数和分布概率是考试要求。理解输出结果并能验证其合理性至关重要。
12. Key Notation & Memory Aids | 关键符号与记忆技巧
Here is a quick-reference table of the most tested symbols:
以下是常考符号的速查表：
| μ (mu) – population mean 总体均值 | σ (sigma) – population standard deviation 总体标准差 |
| σ² – population variance 总体方差 | x̄ – sample mean 样本均值 |
| s² – sample variance 样本方差 | r – PMCC 积矩相关系数 |
| ρ (rho) – population correlation coefficient 总体相关系数 | χ² – chi-squared statistic 卡方统计量 |
| ν (nu) – degrees of freedom 自由度 | α (alpha) – significance level 显著性水平 |
Create mental connections: ‘μ’ looks like the mast of a ship — the ‘mean’ ship. ‘σ’ wiggles like the spread of data. ‘r’ for relationship. Visual mnemonics make recall faster under exam pressure.
建立心理联结：’μ’ 看起来像船上的桅杆，联想到“均值之船”；’σ’ 形状如数据的散布；’r’ 代表关系。图像化记忆法能让你在考试压力下更快地回想起来。
Published by TutorHao | Statistics Revision Series | aleveler.com
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