📚 AS WJEC Statistics: Quick Vocabulary & Terminology Guide | AS WJEC 统计：词汇术语速记指南
Statistics can feel like learning a new language, especially when you are expected to define terms precisely and apply them correctly under exam conditions. This guide breaks down the core vocabulary you’ll meet in the AS WJEC Statistics specification, pairing every concept with a memorable explanation in both English and Chinese. Use it alongside your regular revision to build confidence with the terminology that often carries as many marks as the calculations themselves.
统计有时就像学一门新语言，尤其在考试中需要精准定义术语并正确运用时更是如此。本指南拆解 WJEC AS 统计考纲中的核心词汇，每个概念都附有中英双语解释，方便记忆。配合日常复习使用，你就能更从容地掌握那些和计算题同样占分的术语类问题。
1. Data Types and Collection | 数据类型与收集
Quantitative data are numerical values that represent counts or measurements. They can be discrete (e.g. number of students in a class) or continuous (e.g. height of a plant).
定量数据是表示计数或测量的数值，可以分为离散（例如班级学生人数）和连续（例如植物的高度）。
Qualitative data describe categories or characteristics and are sometimes called categorical data. They are not naturally numerical, like eye colour or types of fruit.
定性数据描述类别或特征，也称为分类数据，不是天生的数值，比如眼睛颜色或水果种类。
Primary data are collected first-hand by the researcher for a specific purpose. Secondary data are gathered from existing sources such as government records or previous studies.
一手数据由研究者为特定目的直接收集；二手数据来自已有资料，如政府记录或过往研究。
A population is the entire set of individuals or items that you want to investigate. A sample is a subset of the population selected for the actual study.
总体是你想研究的全部个体或项目集合；样本是从总体中选出用于实际研究的子集。
2. Measures of Central Tendency | 集中趋势度量
The mean is the arithmetic average, calculated by summing all data values and dividing by the number of observations. For a sample it is denoted x̄, for a population μ.
平均数是算术平均值，用所有数据之和除以观测值个数算得。样本平均数记作 x̄，总体平均数记作 μ。
The median is the middle value when the data are arranged in order. For an even number of observations, it is the midpoint of the two central values.
中位数是将数据排序后位于中间的值；若观测值个数为偶数，则取中间两个数值的平均。
The mode is the most frequently occurring value in a data set. A set of data may have no mode, one mode, or more than one mode (bimodal).
众数是数据集中出现频率最高的值。一组数据可能没有众数、有一个众数或多个众数（双众数）。
For grouped data, the modal class is the interval with the highest frequency. You can estimate the mean from grouped data using midpoints of class intervals.
对于分组数据，众数组是频数最高的区间；可以用组中值来估计分组数据的平均数。
3. Measures of Dispersion | 离散程度度量
The range is the simplest measure of spread: maximum value − minimum value. It is easily affected by outliers.
极差是最简单的离散度量，等于最大值减最小值，容易受极端值影响。
The interquartile range (IQR) is the difference between the upper quartile Q₃ and the lower quartile Q₁, covering the middle 50% of the data. It is robust to outliers.
四分位距 (IQR) 是上四分位数 Q₃ 与下四分位数 Q₁ 之差，涵盖中间 50% 的数据，对异常值稳健。
Variance measures the average squared deviation from the mean. For a sample, s² = Σ(x − x̄)²/(n−1). For a population, σ² = Σ(x−μ)²/N.
方差衡量数据与平均数之差的平方的平均值。样本方差 s² = Σ(x−x̄)²/(n−1)，总体方差 σ² = Σ(x−μ)²/N。
Standard deviation is the square root of the variance, returning the measure to the original units of the data. It is widely used with the mean.
标准差是方差的平方根，将度量单位还原为数据原单位，常与平均数一起使用。
4. Probability Basics | 概率基础
The probability of an event A, written P(A), is a number between 0 and 1 that measures how likely the event is to occur. 0 means impossible, 1 means certain.
事件 A 的概率记作 P(A)，是一个介于 0 到 1 之间的数，表示事件发生的可能性大小。0 表示不可能，1 表示必然。
Mutually exclusive events cannot happen at the same time. If A and B are mutually exclusive, then P(A ∩ B) = 0 and P(A ∪ B) = P(A) + P(B).
互斥事件不能同时发生。若 A 与 B 互斥，则 P(A ∩ B) = 0 且 P(A ∪ B) = P(A) + P(B)。
Independent events are those where the occurrence of one does not affect the probability of the other. For independent events A and B, P(A ∩ B) = P(A) × P(B).
独立事件中，一个事件的发生不影响另一个事件发生的概率。若 A 与 B 独立，则 P(A ∩ B) = P(A) × P(B)。
A sample space is the set of all possible outcomes of an experiment. A tree diagram is often used to display multi-stage experiments.
样本空间是实验所有可能结果的集合。多阶段实验常用树状图来展示结果。
5. Discrete Random Variables | 离散随机变量
A discrete random variable X takes a countable number of distinct values, each with an associated probability. The sum of all probabilities P(X=x) must equal 1.
离散随机变量 X 取可数个不同的值，每个值有一个对应的概率，所有概率之和必须等于 1。
The expected value E(X) or μ is the long-run average value of the random variable, calculated as Σ [x × P(X=x)].
期望值 E(X) 或 μ 是随机变量的长期平均值，计算公式为 Σ [x × P(X=x)]。
The variance of a discrete random variable is Var(X) = Σ [x² P(X=x)] − [E(X)]². The standard deviation is √Var(X).
离散随机变量的方差为 Var(X) = Σ [x² P(X=x)] − [E(X)]²，标准差为 √Var(X)。
A probability mass function (PMF) lists each possible value of the discrete random variable and its probability. It can be displayed as a table or a bar chart.
概率质量函数列出离散随机变量的每个可能取值及其概率，可用表格或条形图表示。
6. Binomial Distribution | 二项分布
The binomial distribution X ~ B(n, p) models the number of successes in n independent trials, each with the same probability of success p. The trials must be independent and identical.
二项分布 X ~ B(n, p) 描述 n 次独立试验中成功的次数，每次试验的成功概率 p 相同。试验必须独立且条件一致。
The probability of exactly r successes is given by P(X=r) = ⁿCᵣ pʳ (1−p)ⁿ⁻ʳ, where ⁿCᵣ = n! / [r!(n−r)!].
恰好 r 次成功的概率为 P(X=r) = ⁿCᵣ pʳ (1−p)ⁿ⁻ʳ，其中 ⁿCᵣ = n! / [r!(n−r)!]。
The expected value of a binomial random variable is E(X) = np, and the variance is Var(X) = np(1−p).
二项随机变量的期望值为 E(X) = np，方差为 Var(X) = np(1−p)。
You can use cumulative binomial probability tables or a calculator to find P(X ≤ r) or P(X ≥ r). Make sure you know how to use the table for both ≤ and ≥ forms.
可以使用累积二项分布概率表或计算器求 P(X ≤ r) 或 P(X ≥ r)。务必掌握如何查表处理 ≤ 和 ≥ 两种形式。
7. Normal Distribution | 正态分布
The normal distribution is a continuous probability distribution that is symmetric and bell-shaped. It is written as X ~ N(μ, σ²), where μ is the mean and σ² is the variance.
正态分布是一种对称的钟形连续概率分布，记作 X ~ N(μ, σ²)，其中 μ 是平均数，σ² 是方差。
To work with the normal distribution, we standardize to the standard normal variable Z ~ N(0, 1) using Z = (X − μ) / σ.
为使用正态分布，我们通过 Z = (X − μ) / σ 将变量标准化为标准正态变量 Z ~ N(0, 1)。
The 68-95-99.7 rule states that approximately 68% of data lie within 1σ of μ, 95% within 2σ, and 99.7% within 3σ.
68-95-99.7 法则指出，约 68% 的数据落在 μ±1σ 内，95% 落在 μ±2σ 内，99.7% 落在 μ±3σ 内。
Use normal distribution tables to find probabilities like P(Z < z). Remember that the total area under the curve is 1, and that P(Z > z) = 1 − P(Z < z).
利用正态分布表可查找如 P(Z < z) 的概率。记住曲线下总面积为 1，且 P(Z > z) = 1 − P(Z < z)。
When approximating a binomial distribution with a normal distribution (when np and nq are large enough), you must apply a continuity correction.
当用正态分布近似二项分布时（np 与 nq 足够大），必须使用连续性校正。
8. Sampling Methods | 抽样方法
A simple random sample gives every member of the population an equal chance of being selected, often using random number generators or drawing lots.
简单随机抽样使总体中每个成员被选中的机会均等，常用随机数生成器或抽签实现。
Stratified sampling divides the population into distinct groups (strata) and then takes a random sample from each stratum proportionally or equally. This ensures representation.
分层抽样将总体分成不同的层，然后从每层按比例或均匀抽取随机样本，从而保证代表性。
Systematic sampling selects every kth member from a list after a random starting point. It is simple but may introduce bias if there is an underlying pattern.
系统抽样是随机确定起点后，每隔 k 个抽取一个样本。方法简单，但如果名单中存在隐含模式，可能引入偏差。
Cluster sampling divides the population into clusters, then randomly selects whole clusters to be sampled. It is useful when a population is geographically spread out.
整群抽样将总体分成若干群，然后随机抽取整群作为样本。适用于地理分布广泛的总体。
Opportunity (convenience) sampling uses individuals who are readily available. It is quick and cheap, but likely to be biased and not representative.
便利抽样选取最容易接触到的人作为样本，快速省钱，但很可能存在偏差、不具代表性。
9. Data Representation | 数据表示
A frequency table organises data by listing each value (or class) alongside how many times it occurs. It is the starting point for most diagrams.
频数表将数据按数值（或组别）列出并标明出现次数，是大多数图表的基础。
Histograms are used for continuous data or grouped discrete data, where the area of each bar is proportional to the frequency. Unlike bar charts, bars touch each other to show continuous scale.
直方图用于连续数据或分组离散数据，每个柱形的面积与频数成正比。与条形图不同，直方图的柱形相互接触以体现连续性。
A box-and-whisker plot (or boxplot) displays the minimum, Q₁, median, Q₃, and maximum values. It is excellent for comparing spreads and identifying outliers.
箱线图展示最小值、Q₁、中位数、Q₃ 和最大值，非常利于比较离散程度和识别异常值。
Cumulative frequency graphs plot the running total of frequencies against the upper class boundary. Medians and quartiles can be estimated from the curve.
累积频数图将频数的累计和标绘在上组界上，可从曲线上估计中位数和四分位数。
A scatter diagram shows the relationship between two variables. It gives a visual clue about the type and strength of correlation before you calculate any coefficients.
散点图展示两个变量之间的关系，在计算相关系数前就能直观看出相关的类型和强度。
10. Correlation and Regression | 相关与回归
Correlation describes the strength and direction of a linear relationship between two variables. It does not imply causation.
相关描述两个变量之间线性关系的强度和方向，并不意味着因果关系。
The product moment correlation coefficient (PMCC), denoted by r, measures linear correlation. Values range from −1 (perfect negative) to +1 (perfect positive). r = 0 indicates no linear correlation.
积差相关系数 r 衡量线性相关，取值从 −1（完全负相关）到 +1（完全正相关）。r = 0 表示无线性相关。
A regression line (least squares regression line) models the relationship by y = a + bx, where b is the gradient and a is the y‑intercept. It is used to predict y from x.
回归直线（最小二乘回归线）用 y = a + bx 建立关系模型，其中 b 是斜率，a 是截距。用于由 x 预测 y。
The explanatory variable (independent variable) is plotted on the x-axis. The response variable (dependent variable) is the one we predict or explain, plotted on the y-axis.
解释变量（自变量）绘制在 x 轴上；响应变量（因变量）是我们预测或解释的变量，绘制在 y 轴上。
Interpolation means predicting inside the range of observed data; extrapolation means predicting outside that range. Extrapolation is unreliable because the pattern may change beyond the observed data.
内插是在观测数据范围内作预测；外推则超出该范围。外推不可靠，因为超出数据范围的模式可能发生变化。
Published by TutorHao | Statistics Revision Series | aleveler.com
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