📚 Year 12 Edexcel Statistics: Glossary & Memory Guide | Year 12 Edexcel 统计：词汇术语速记指南
Mastering the vocabulary of statistics is half the battle in Year 12 Edexcel. This bilingual guide covers the essential terms you will meet in data handling, probability, sampling, correlation, regression, and the normal distribution. Each entry pairs an English definition with its Chinese equivalent, plus a memory tip to help you recall the meaning quickly under exam pressure. Read on to turn confusing jargon into clear, connected concepts.
掌握统计学词汇是征服 Year 12 Edexcel 统计的关键一步。这份双语指南涵盖了数据处理、概率、抽样、相关回归以及正态分布中的核心术语。每个条目都配有中英文定义和速记提示，帮助你在考试压力下快速回忆含义。让我们把混乱的行话转化为清晰连贯的概念。
1. Population and Sample | 总体与样本
Population is the complete collection of all individuals or items that we want information about. Think ‘the whole picture’.
总体是我们希望获取信息的所有个体或项目的完整集合。牢记 ‘整幅图画’。
Sample is a subset of the population selected to represent it. A sample must be chosen carefully to avoid bias. Think ‘snapshot’.
样本是从总体中选出的一个子集，用以代表总体。样本选择必须审慎，避免偏差。牢记 ‘快照’。
Sampling frame is a list of all members of the population from which the sample is drawn. If the frame is incomplete, the sample may be biased.
抽样框是列出总体所有成员的清单，样本由此抽取。如果抽样框不完整，样本便可能产生偏差。
Census collects data from every member of the population. It can be very accurate but is often impractical and expensive.
普查收集总体中每一个体的数据。结果可以非常精确，但常常因成本高昂而不切实际。
2. Parameter and Statistic | 参数与统计量
Parameter is a numerical measure that describes a characteristic of a population. For example, the population mean μ is a parameter. We rarely know its true value.
参数是描述总体某个特征的数值度量。例如总体均值 μ 就是一个参数。我们很少知道它的真实值。
Statistic is a numerical measure calculated from a sample, used to estimate a parameter. The sample mean x̄ is a statistic.
统计量是从样本计算出的数值度量，用于估计参数。样本均值 x̄ 就是一个统计量。
Memory aid: ‘P’ in Parameter goes with ‘P’ in Population; ‘S’ in Statistic goes with ‘S’ in Sample. This pairing never fails.
记忆技巧：Parameter 里的 ‘P’ 对应 Population 的 ‘P’；Statistic 里的 ‘S’ 对应 Sample 的 ‘S’。这个对应关系百试不爽。
3. Types of Variables | 变量类型
Categorical (qualitative) variable: data that can be sorted into non‑numerical groups. Examples: eye colour, type of car. Categorical variables can be nominal (no order) or ordinal (natural order).
分类变量（定性变量）：数据可以归入非数值的组别。例如眼睛颜色、汽车类型。分类变量可分为名义变量（无顺序）或有序变量（有自然顺序）。
Numerical (quantitative) variable: data that are numbers and represent a measurable quantity. Two subtypes: discrete and continuous.
数值变量（定量变量）：数据为数字，表示可测量的量。分成两种子类型：离散型和连续型。
Discrete variable can only take certain isolated values, often whole numbers. Example: number of students in a class. Think ‘counted’.
离散变量只能取特定的、孤立的数值，通常是整数。例如一个班级的学生人数。记住 ‘可数的’。
Continuous variable can take any value within a given range. Example: height, time, temperature. Think ‘measured, not counted’.
连续变量可以在给定范围内取任意值。例如身高、时间、温度。记住 ‘测量出而非数出来’。
4. Measures of Central Tendency | 集中趋势的度量
Mean (average): sum of all values divided by the number of values. It uses every data point, so it is sensitive to outliers. For a sample we denote it x̄; for a population we use μ.
均值（平均数）：所有数值之和除以数值的个数。它使用了每一个数据点，因此对异常值敏感。样本均值记作 x̄，总体均值记作 μ。
Median: the middle value when the data are arranged in order. It is unaffected by extreme values. For n data values, position = (n+1)/2.
中位数：将数据按顺序排列后居中的值。它不受极端值影响。对于 n 个数据，位置为 (n+1)/2。
Mode: the value that occurs most frequently. A data set can have one mode, more than one mode, or no mode at all. Useful for categorical data.
众数：出现频率最高的值。数据集可能有一个、多个或没有众数。非常适用于分类数据。
Tip: To remember which measure is resistant to outliers, think ‘Median stays in the Middle’.
贴士：要记住哪种度量不受离群值影响，就记 ‘Median 稳稳守在 Middle’。
5. Measures of Dispersion | 离散程度的度量
Range: the difference between the largest and smallest values. Quick to compute but easily distorted by a single outlier.
极差（全距）：最大值与最小值的差。计算迅速，但容易被一个离群值严重扭曲。
Interquartile range (IQR): the difference between the upper quartile (Q₃) and the lower quartile (Q₁). IQR measures the spread of the middle 50% of the data, making it robust to outliers.
四分位距 (IQR)：上四分位数 (Q₃) 与下四分位数 (Q₁) 之差。IQR 衡量中间 50% 数据的分散程度，对离群值稳健。
Variance and standard deviation measure how far the data values are spread around the mean. Standard deviation is the square root of variance. A small standard deviation means data are tightly clustered around the mean.
方差与标准差衡量数据值围绕均值的分布广度。标准差是方差的平方根。标准差小意味着数据紧密聚集在均值周围。
Outlier: an observation that lies an abnormal distance from other values. A common rule is any value below Q₁ − 1.5×IQR or above Q₃ + 1.5×IQR.
离群值（异常值）：与其他值存在异常距离的观测值。一个常用规则是任何小于 Q₁ − 1.5×IQR 或大于 Q₃ + 1.5×IQR 的值。
6. Probability Fundamentals | 概率基础
Experiment: a repeatable process that gives rise to a set of outcomes. Outcome: a single possible result. Event: a collection of one or more outcomes.
试验：可重复进行、产生一系列结果的过程。结果：单个可能的结果。事件：一个或多个结果的集合。
Sample space: the set of all possible outcomes of an experiment. Usually denoted S. The probability of the whole sample space is 1.
样本空间：试验所有可能结果的集合。通常记为 S。整个样本空间的概率为 1。
Mutually exclusive events cannot happen at the same time. For such events, P(A ∪ B) = P(A) + P(B).
互斥事件不可能同时发生。对于互斥事件，P(A ∪ B) = P(A) + P(B)。
Independent events: the occurrence of one does not affect the probability of the other. The test: P(A ∩ B) = P(A) × P(B).
独立事件：一个事件的发生不影响另一个事件的概率。检验：P(A ∩ B) = P(A) × P(B)。
Memory: ‘sex’ (Mutually Exclusive) means ‘can’t happen together’, while ‘Independence’ means ‘no Influence’.
记忆：互斥（Mutually Exclusive）意味着 ‘不能同时’，独立（Independent）意味着 ‘不影响’。
7. Sampling Methods | 抽样方法
Simple random sampling: every member of the population has an equal chance of being selected. Often using a random number generator. Avoids bias but needs a sampling frame.
简单随机抽样：总体中每个成员被选中的概率相等。常使用随机数生成器。可避免偏差但需要抽样框。
Stratified sampling: population is divided into groups (strata), and a random sample is taken from each stratum in proportion to its size. Ensures representation of all key subgroups.
分层抽样：将总体分成若干层，然后按各层大小比例从每层随机抽取样本。确保所有关键子群都有代表。
Systematic sampling: choose every k-th item from the sampling frame after a random start. Easy to use but can introduce periodicity bias.
系统抽样：在随机起点后，从抽样框中每隔 k 个抽取一个。简便易行，但可能引入周期性偏差。
Quota sampling: interviewers select a fixed number of people from different categories (e.g. age, gender). No sampling frame needed, but selection bias is possible.
配额抽样：访问员从不同类别（如年龄、性别）中选取固定人数。不需要抽样框，但可能存在选择偏差。
Opportunity (convenience) sampling: sample is taken from people who are available at the time. Quick and cheap, but often highly unrepresentative.
便利抽样（机会抽样）：样本从当时方便接触到的人群中抽取。快速且成本低，但通常代表性极差。
8. Correlation and Regression | 相关与回归
Scatter diagram: a graph of plotted points showing the relationship between two variables. It can suggest positive, negative or no correlation.
散点图：显示两个变量关系的点图。可体现正相关、负相关或无相关。
Correlation coefficient (r): a measure of the strength and direction of a linear relationship. r always lies between −1 and 1. r = 1: perfect positive; r = −1: perfect negative; r = 0: no linear correlation.
相关系数 (r)：衡量线性关系强度与方向的量。r 始终在 −1 到 1 之间。r = 1 完全正相关；r = −1 完全负相关；r = 0 无线性相关。
Regression line (y = a + bx): the ‘line of best fit’ that minimises the sum of squared residuals. b is the slope; a is the intercept. Used to predict y from x.
回归直线 (y = a + bx)：最小化残差平方和的 ‘最佳拟合线’。b 为斜率，a 为截距。用于从 x 预测 y。
Interpolation: predicting inside the range of the observed data. Generally reliable. Extrapolation: predicting outside the range. It can be dangerous because the linear pattern may not continue.
内插：在观测数据范围内进行预测，通常可靠。外推：在范围之外进行预测。可能有风险，因为线性模式未必延续。
9. Data Presentation | 数据展示
Histogram: a diagram for grouped continuous data, where area of each bar is proportional to frequency. The vertical axis is frequency density = frequency ÷ class width.
直方图：用于分组连续数据的图形，每一条的面积与频数成比例。纵轴为频率密度 = 频数 ÷ 组距。
Cumulative frequency curve: a graph showing the running total of frequencies. Used to estimate medians, quartiles and percentiles by interpolation.
累积频率曲线：展示频次累计和的图形。可用于通过插值估计中位数、四分位数和百分位数。
Box plot (box-and-whisker): a visual summary showing minimum, Q₁, median, Q₃ and maximum. Outliers may be plotted separately. Ideal for comparing distributions.
箱线图（盒须图）：展示最小值、Q₁、中位数、Q₃ 和最大值的可视化摘要。离群值可单独标出。适合比较分布。
Stem-and-leaf diagram: a display that keeps the original data values while showing the shape of the distribution. The ‘stem’ is the leading digit(s), the ‘leaf’ the final digit.
茎叶图：保留原始数据值的同时展示分布形状的图形。’茎’ 为前导数字，’叶’ 为最后一位数字。
10. The Normal Distribution | 正态分布
Normal distribution: a continuous probability distribution with a bell‑shaped curve. It is symmetric about the mean μ, and the spread is determined by the standard deviation σ.
正态分布：具有钟形曲线的连续概率分布。关于均值 μ 对称，分散程度由标准差 σ 决定。
Empirical rule (68–95–99.7%): about 68% of data lie within 1σ of μ, 95% within 2σ, and 99.7% within 3σ. Useful for quick estimates in exam problems.
经验法则（68-95-99.7%）：约 68% 的数据落在 μ ± 1σ 内，95% 在 μ ± 2σ 内，99.7% 在 μ ± 3σ 内。有助于在考试中快速估算。
Standard normal distribution: a normal distribution with μ = 0 and σ = 1. Any normal variable X can be standardised using z = (x − μ) / σ. The z‑score tells you how many standard deviations x is from the mean.
标准正态分布：均值为 0、标准差为 1 的正态分布。任意正态变量 X 可通过 z = (x − μ) / σ 进行标准化。z 分数表示 x 距离均值有多少个标准差。
11. Common Symbols and Notation | 常见符号与记号
| Symbol | English meaning | 中文含义 |
|---|---|---|
| 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 |
| Σ | Summation (‘add them up’) | 求和（’全部加起来’） |
| Q₁, Q₂, Q₃ | Lower quartile, median, upper quartile | 下四分位数、中位数、上四分位数 |
| IQR | Interquartile range = Q₃ − Q₁ | 四分位距 |
| r | Product‑moment correlation coefficient | 积矩相关系数 |
| a, b | Regression line coefficients (intercept, slope) | 回归直线系数（截距、斜率） |
| z | Standardised normal score | 标准正态得分 |
Remembering these symbols accelerates your exam fluency. Write them on a flashcard and test yourself daily.
记住这些符号能提升你的考试熟练度。把它们写在记忆卡上，每天自测一次。
12. Key Exam Tips and Mnemonics | 考试要点与记忆助词
Use the phrase ‘S unday M orning C offee’ for S ampling M ethods C omparison: think of Simple, Stratified, Systematic, Quota, Opportunity (convenience) – the five major sampling techniques you need to describe and evaluate.
用短语 ‘S unday M orning C offee’ 记住五种主要抽样方法：Simple, Stratified, Systematic, Quota, Opportunity（便利）——这些是要求你会描述和评价的方法。
For the normal distribution, the phrase ‘Z ebra E scapes S afari’ reminds you: Z = (X − μ) / σ . And ’68, 95, 99.7′ can be recalled as ‘S ong 68, feel alive; 95, almost arrive; 99.7, near heaven’.
对于正态分布，短语 ‘Z ebra E scapes S afari’ 让你记住：Z = (X − μ) / σ。而 ’68, 95, 99.7′ 可联想为 ’68 不离身，95 渐接近，99.7 近完美’。
When interpreting correlation, remember: correlation does not imply causation. Just because two variables move together does not mean one causes the other.
解释相关关系时务必牢记：相关关系不代表因果关系。两个变量同向变动，并不意味一个导致了另一个。
Finally, always define variables, show working, and comment on reliability when answering statistical questions. Clear terminology earns marks even if calculations slip.
最后，回答统计问题时一定要定义变量、展示运算过程，并对可靠性加以评述。清晰的术语运用即使在计算有误时也能为你赢得分数。
Published by TutorHao | Statistics Revision Series | aleveler.com
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