AS Eduqas Statistics: Key Terminology Quick-Reference | AS Eduqas 统计：词汇术语速记指南

📚 AS Eduqas Statistics: Key Terminology Quick-Reference | AS Eduqas 统计：词汇术语速记指南

Mastering the technical language of statistics is as important as solving numerical problems. This guide compiles the essential terms you will encounter in the AS Eduqas Statistics syllabus, providing concise definitions and memory aids to help you recall them quickly during revision and exams.

掌握统计学的专业术语与解题技巧同样重要。本指南汇编了 AS Eduqas 统计大纲中你需要掌握的核心术语，提供简洁的定义和记忆要点，帮助你在复习和考试中迅速调用。

1. Key Statistical Terms & Population vs Sample | 基本统计术语与总体和样本

Population – the complete collection of all the items that are of interest in a statistical investigation. Think of it as the ‘whole group’.

总体 – 统计调查中所有感兴趣个体的完整集合。可理解为“全组”。

Sample – a subset of the population selected for the actual study. It should be representative to allow valid inferences.

样本 – 从总体中选出的用于实际研究的一个子集。样本必须具有代表性，才能得出有效的推断。

Census – data collected from every member of the population. Often impractical for large populations.

普查 – 收集总体中每一个成员的数据。对大型总体往往不可行。

Sampling frame – a list of all members of the population from which the sample is drawn, e.g. a register of students.

抽样框 – 总体全部成员的一个列表，样本从中抽取，例如学生名册。

Parameter – a numerical measure that describes a characteristic of a population, such as the population mean μ. Memory tip: Parameter and Population both start with ‘P’.

参数 – 描述总体某一特征的数值度量，如总体均值 μ。记忆提示：参数与总体都以字母 P 开头。

Statistic – a numerical measure calculated from a sample, used to estimate a population parameter, such as the sample mean x̄. Memory tip: Statistic and Sample both start with ‘S’.

统计量 – 由样本计算得出的数值度量，用于估计总体参数，如样本均值 x̄。记忆提示：统计量与样本都以字母 S 开头。

Variable – any characteristic that can take different values for different individuals, e.g. height or exam score.

变量 – 在不同个体身上可取不同值的任何特征，如身高或考试成绩。

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2. Types of Data | 数据类型

Qualitative (categorical) data – non-numerical data that describe attributes or categories, such as hair colour, type of car, or exam grade (A, B, C).

定性（分类）数据 – 描述属性或类别的非数值型数据，如发色、汽车型号或考试等级 (A, B, C)。

Quantitative (numerical) data – data that are numbers obtained by measuring or counting, such as height, temperature, or number of pets.

定量（数值型）数据 – 通过测量或计数得到的数字数据，如身高、温度、宠物数量。

Quantitative data can be further split:

定量数据可进一步分为：

Discrete data – can only take certain, usually integer, values (e.g. number of students, goals scored, shoe size). There are gaps between values.

离散数据 – 只能取某些特定的、通常是整数的值（如学生人数、进球数、鞋码）。数值之间存在间隔。

Continuous data – can take any value within a given range, measured on a continuous scale (e.g. weight, time, length).

连续数据 – 可以在给定范围内取任何值，在连续尺度上测量（如体重、时间、长度）。

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3. Sampling Methods | 抽样方法

Selecting a sample properly is crucial to avoid bias. Here are the main techniques required in AS Eduqas Statistics:

正确选择样本对于避免偏误至关重要。以下是 AS Eduqas 统计中要求的主要抽样方法：

Method	English Description	中文描述
Simple random	Every member of the population has an equal chance of being selected, e.g. using a random number generator.	总体中每个成员被抽中的机会均等，例如使用随机数生成器。
Systematic	Choose every kth member from the sampling frame after a random start.	随机确定起点后，每隔固定间隔 k 抽取一个样本。
Stratified	Divide the population into distinct groups (strata) and take a random sample from each stratum proportional to its size.	将总体分成不同的层，然后按各层大小比例从每层中随机抽样。
Opportunity (convenience)	Sample chosen from people who are readily available, e.g. asking classmates. Prone to bias.	从容易接触到的人群中抽取样本，例如询问同学。容易产生偏误。
Quota	Interviewers are given quotas for different categories (e.g. age, gender) and then select any individuals to fill them; not random.	访问员被分配各类别的名额（如年龄、性别），然后自行选择个体填满名额；非随机抽样。

Bias – when a sample does not fairly represent the population, leading to systematic error in conclusions. Avoid by using random methods and a suitable sampling frame.

偏误 – 当样本不能公平代表总体时，导致结论出现系统误差。应通过随机方法和合适的抽样框来避免。

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4. Measures of Central Tendency | 中心趋势度量

Mean – the arithmetic average. For a sample: x̄ = Σx / n. For a population: μ = Σx / N. It uses all data but is sensitive to outliers.

均值 – 算术平均数。样本均值：x̄ = Σx / n。总体均值：μ = Σx / N。均值利用所有数据，但对异常值敏感。

Median – the middle value when the data are ordered. For n numbers, it is the (n+1)/2 th value. Unaffected by extreme values.

中位数 – 数据排序后正中间的值。对于 n 个数，位于第 (n+1)/2 个。不受极端值影响。

Mode – the value that occurs most frequently. A data set may have no mode, one mode (unimodal) or more than one mode. Can be used for qualitative data.

众数 – 出现频率最高的值。一组数据可能没有众数、一个众数（单峰）或多个众数。可用于定性数据。

Memory tip: The three M’s — Mean uses Mathematics, Median is the Middle, Mode is the Most frequent.

记忆提示：三个 M —— Mean 计算数学期望（Mathematics），Median 取中间（Middle），Mode 取最常见的（Most）。

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5. Measures of Dispersion | 离散度量

Range = maximum value − minimum value. Simple but ignores the spread of middle data.

极差 = 最大值 − 最小值。简单但忽略了中间数据的分布。

Interquartile range (IQR) = Q₃ − Q₁. It measures the spread of the middle 50% and is resistant to outliers.

四分位距 (IQR) = Q₃ − Q₁。衡量中间 50% 数据的分散程度，不受异常值影响。

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. The sample variance uses n−1 to give an unbiased estimator.

方差 衡量数据与均值离差平方的平均程度。样本方差：s² = Σ(x − x̄)² / (n − 1)。总体方差：σ² = Σ(x − μ)² / N。样本方差分母用 n−1 以得到无偏估计量。

Standard deviation is the square root of the variance: s = √s² or σ = √σ². It is in the same units as the original data, making it easier to interpret.

标准差 是方差的平方根：s = √s² 或 σ = √σ²。它与原数据单位相同，易于解释。

Memory tip: Variance is the ‘square’ of standard deviation; if you need

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