AS AQA Statistics: Quick Guide to Memorising Key Terms | AS AQA 统计：词汇术语速记指南

📚 AS AQA Statistics: Quick Guide to Memorising Key Terms | AS AQA 统计：词汇术语速记指南

Welcome to your fast-track guide for mastering the key vocabulary of AS AQA Statistics. This resource breaks down every essential term into clear English definitions paired with Chinese translations, grouped by topic to help you memorise them quickly. Use these explanations alongside your revision notes to build confidence with statistical language and ace your exam.

欢迎使用这本 AS AQA 统计核心词汇速记指南。我们按主题把每个重要术语都整理成了清晰的英文定义与中文翻译，帮助你快速记忆。请将这些解释与你的课堂笔记结合使用，牢固掌握统计语言，自信应对考试。

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1. Populations and Samples | 总体与样本

Population is the entire set of items or individuals of interest in a statistical investigation. The sample is a smaller subset selected from the population to represent it. A census collects data from every member of the population, whereas a sample survey collects data only from the sample.

总体是统计调查中关注的全部项目或个体的集合。样本是从总体中选出的用于代表总体的较小子集。普查从总体的每一个成员收集数据，而抽样调查仅从样本收集数据。

The sampling unit is each individual element available for selection, and the sampling frame is a full list of all sampling units from which the sample is drawn. A perfect sampling frame covers the whole population, but often it is incomplete or inaccurate.

抽样单位是可供选择的每个个体元素，抽样框是所有抽样单位的完整名单，样本即从中抽出。理想的抽样框覆盖整个总体，但往往存在遗漏或不准确的情况。

A parameter is a numerical summary of a population (e.g. population mean μ), whereas a statistic is a numerical summary calculated from a sample (e.g. sample mean x̄). Parameters are usually unknown and are estimated by statistics.

参数是总体的数值概括（如总体均值 μ），统计量则是从样本计算得到的数值概括（如样本均值 x̄）。参数通常未知，需要由统计量来估计。

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2. Types of Data | 数据类型

Qualitative (or categorical) data describe qualities or attributes and are non-numerical – for example, eye colour or type of vehicle. Quantitative data are numerical and can be further split into discrete and continuous. Think ‘Quality vs Quantity’ to keep them apart.

定性（或分类）数据描述性质或属性，是非数值的——例如眼睛颜色或车辆类型。定量数据是数值型的，并可进一步分为离散数据和连续数据。用“质与量”来区分它们非常简单。

Discrete data arise from counting and can only take certain separated values, often whole numbers – number of students, goals scored. Continuous data come from measuring and can take any value within a given interval – height, time, temperature. Remember: discrete can be counted on fingers, continuous flows like a measuring tape.

离散数据通过计数得到，只能取某些分离的数值，通常是整数——如学生人数、进球数。连续数据通过测量得到，可以在某一区间内取任意值——如身高、时间、温度。记住：离散可以用手指点着数，连续像卷尺一样可以不断细分。

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3. Measures of Central Tendency | 集中趋势度量

The mean (often x̄ for a sample, μ for a population) is the arithmetic average: sum all values and divide by the number of items. It is sensitive to extreme values (outliers). The median is the middle value when data are ordered; it is not pulled by outliers, making it a better average for skewed distributions.

均值（样本常记作 x̄，总体记作 μ）是算术平均值：所有数据之和除以数据个数。它对极端值（离群值）敏感。中位数是排序后位于中间位置的数值；它不受极端值影响，因此在偏态分布中是一个更好的平均度量。

The mode (or modal class for grouped data) is the value or interval that occurs most frequently. A data set can have more than one mode. For symmetric unimodal distributions, mean = median = mode; for positively skewed data, mean > median > mode; for negatively skewed, mean < median < mode.

众数（分组数据中用众数区间）是出现频率最高的值或区间。一组数据可以有多个众数。在对称单峰分布中，均值=中位数=众数；正偏态时，均值 > 中位数 > 众数；负偏态时，均值 < 中位数 < 众数。

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4. Measures of Dispersion | 离散程度度量

The range is the simplest measure: maximum minus minimum. It is strongly affected by outliers. The interquartile range (IQR) = Q₃ − Q₁, where Q₁ is the lower quartile (25th percentile) and Q₃ is the upper quartile (75th percentile). IQR focuses on the middle 50% and is resistant to outliers.

极差是最简单的度量：最大值减最小值。它极易受离群值影响。四分位距（IQR）= Q₃ − Q₁，其中 Q₁ 是下四分位数（第25百分位数），Q₃ 是上四分位数（第75百分位数）。IQR 关注中间50%的数据，对离群值不敏感。

Variance measures the average squared deviation from the mean. For a population: σ² = Σ(x − μ)² / N. For a sample: s² = Σ(x − x̄)² / (n − 1). The standard deviation is the square root of the variance and has the same units as the raw data. Quick aide: variance is ‘squared spread’, standard deviation is ‘typical spread’.

方差衡量数据偏离均值的平方的平均。总体方差：σ² = Σ(x − μ)² / N。样本方差：s² = Σ(x − x̄)² / (n − 1)。标准差是方差的平方根，与原数据的单位相同。简单记忆：方差是“展布平方”，标准差是“典型展布”。

To find quartiles for discrete data: Q₂ is the median; Q₁ is the median of the lower half; Q₃ the median of the upper half. For grouped data, linear interpolation within intervals is required.

离散数据的四分位数求法：Q₂ 是中位数；Q₁ 是较小那一半数据的中位数；Q₃ 是较大那一半的中位数。分组数据则需在区间内进行线性插值。

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5. Representing Data | 数据表示

A histogram uses area to represent frequency: the area of each bar is proportional to frequency. Frequency density = frequency ÷ class width. Bars touch, unlike bar charts, because the horizontal axis is continuous. Always label frequency density on the vertical axis.

直方图用面积表示频数：每个柱子的面积与频数成比例。频数密度 = 频数 ÷ 组距。与条形图不同，直方图的柱子紧挨在一起，因为横轴是连续变量。纵轴必须标注为频数密度。

A box plot (box-and-whisker diagram) displays minimum, Q₁, median, Q₃ and maximum. Outliers are plotted as individual points, often defined as values below Q₁ − 1.5×IQR or above Q₃ + 1.5×IQR. A cumulative frequency curve lets you read off medians, quartiles and percentiles by interpolation.

箱线图（盒须图）展示最小值、Q₁、中位数、Q₃ 和最大值。离群值单独画为散点，通常的定义是低于 Q₁ − 1.5×IQR 或高于 Q₃ + 1.5×IQR 的数值。累积频数曲线允许你通过插值读出中位数、四分位数和百分位数。

Scatter diagrams show the relationship between two variables. Correlation describes the strength and direction of a linear relationship; it does not imply causation. A line of best fit can be drawn by eye or using a regression line for prediction.

散点图展示两个变量之间的关系。相关描述线性关系的强度和方向；相关并不意味着因果。可以通过目测或回归直线画出最佳拟合线用于预测。

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6. Probability Basics | 概率基础

The sample space (Ω) is the set of all possible outcomes. An event is any subset of the sample space. For any event A, 0 ≤ P(A) ≤ 1. Two events are mutually exclusive if they cannot happen together: P(A ∩ B) = 0, and P(A ∪ B) = P(A) + P(B).

样本空间（Ω）是所有可能结果的集合。事件是样本空间的任意子集。对于任何事件 A，有 0 ≤ P(A

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