GCSE Eduqas Statistics: Vocabulary & Terminology Quick Revision Guide | GCSE Eduqas 统计：词汇术语速记指南

📚 GCSE Eduqas Statistics: Vocabulary & Terminology Quick Revision Guide | GCSE Eduqas 统计：词汇术语速记指南

Mastering the language of statistics is the first step to success in your GCSE Eduqas Statistics exam. This quick revision guide pairs every key term with a clear English definition and its Chinese equivalent, helping you build a bilingual understanding of core concepts. Use it as a memory aid alongside your class notes and past papers.

掌握统计学的语言是你在 GCSE Eduqas 统计考试中取得成功的首要步骤。本速记指南为每个关键术语提供了清晰的英文定义与中文对译，帮助你建立对核心概念的双语理解。可将它作为记忆辅助工具，与课堂笔记和历年真题搭配使用。

1. Types of Data | 数据类型

Data can be classified in various ways, depending on how it is collected and what it represents. Knowing the difference between qualitative and quantitative, discrete and continuous, or primary and secondary data is essential for choosing the right statistical techniques.

数据可以根据收集方式和所代表的含义进行多种分类。了解定性数据与定量数据、离散数据与连续数据、原始数据与二手数据之间的区别，对于选择正确的统计方法至关重要。

Qualitative Data: Non‑numerical data that describes qualities, categories or attributes, e.g. hair colour, favourite sport.

定性数据：描述性质、类别或属性的非数值数据，例如发色、最喜欢的运动。

Quantitative Data: Numerical data that can be measured or counted, e.g. height, test scores.

定量数据：可以测量或计数的数值数据，例如身高、考试分数。

Discrete Data: Quantitative data that can only take specific values, usually whole numbers (e.g. number of cars in a household).

离散数据：只能取特定值（通常是整数）的定量数据，例如家庭汽车数量。

Continuous Data: Quantitative data that can take any value within a given range, e.g. weight, temperature.

连续数据：在给定范围内可以取任意值的定量数据，例如体重、温度。

Primary Data: Data collected by the researcher themselves for a specific investigation.

原始数据：研究者自己为特定调查而收集的数据。

Secondary Data: Data that has already been collected by somebody else, such as government statistics or internet sources.

二手数据：他人已经收集好的数据，例如政府统计数据或网络来源。

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2. Collecting Data | 数据收集

The way data is gathered affects its reliability and validity. In GCSE Statistics you need to recognise different collection methods and sampling techniques, and understand how bias can be introduced.

数据的采集方式会影响其可靠性和有效性。在 GCSE 统计中，你需要识别不同的收集方法和抽样技术，并理解偏差是如何引入的。

Census: A survey that collects data from every member of the population.

普查：从总体中的每一个成员收集数据的调查。

Sample: A subset of the population selected to represent the whole group.

样本：从总体中选出的、用以代表整个群体的子集。

Sampling Frame: A list of all the individuals in the population from which a sample is drawn.

抽样框：总体中所有个体的名单，样本从中抽取。

Simple Random Sampling: Every member of the population has an equal chance of being selected, e.g. using a random number generator.

简单随机抽样：总体中每个成员被选中的概率相等，例如使用随机数生成器。

Stratified Sampling: The population is divided into groups (strata), and a random sample is taken from each stratum in proportion to its size.

分层抽样：将总体分成若干层，然后按各层大小比例从每层中随机抽取样本。

Systematic Sampling: Individuals are selected at regular intervals from the sampling frame, e.g. every 10th name.

系统抽样：从抽样框中按固定间隔选取个体，例如每第 10 个名字。

Bias: A systematic error that causes the sample to be unrepresentative of the population.

偏差：导致样本无法代表总体的系统性误差。

Pilot Study: A small‑scale trial run of a survey or experiment to test procedures and identify problems.

试点研究：调查或实验的小规模预测试，用于检验流程并发现问题。

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

An average summarises the centre of a data set. The three most common averages – mean, median and mode – are used in different situations, and it is important to know which one best represents a given distribution.

平均值可概括数据集的中心。平均数、中位数和众数这三种最常见的平均值适用于不同情形，了解哪个能最好地代表给定分布至关重要。

Mean: The sum of all values divided by the number of values. Often denoted by x̄ for a sample.

平均数：所有数值的总和除以数值的个数。样本平均数常记作 x̄。

Median: The middle value when the data are arranged in order. For an even number of values, it is the mean of the two middle numbers.

中位数：将数据按顺序排列后位于中间的值。如果数值个数为偶数，则取中间两个数的平均值。

Mode: The value that occurs most frequently. A data set can have no mode, one mode (unimodal), or more than one mode (bimodal/multimodal).

众数：出现频率最高的值。一个数据集可以没有众数、有一个众数（单峰）或多个众数（双峰/多峰）。

Modal Class: For grouped data, the class interval with the highest frequency.

众数类：对于分组数据，频数最高的组距。

Estimated Mean for Grouped Data: Calculated using the midpoints of class intervals and their frequencies: x̄ ≈ Σ(fx) / Σf.

分组数据估计平均数：利用组中值及其频数计算：x̄ ≈ Σ(fx) / Σf。

Weighted Mean: An average where some values contribute more than others according to assigned weights.

加权平均数：根据不同权重使某些数值贡献更大的平均值。

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4. Measures of Spread | 离散度量

A measure of spread tells us how scattered or concentrated the data are. Alongside an average, it gives a more complete picture of a distribution. For GCSE Eduqas you need to calculate and interpret range, interquartile range and standard deviation.

离散度量告诉我们数据的分散或集中程度。与平均值结合使用，可更全面地描绘分布。在 Eduqas GCSE 中，你需要计算并解释全距、四分位距和标准差。

Range: The difference between the largest and smallest values: Range = max − min.

全距：最大值与最小值之差：全距 = 最大值 − 最小值。

Interquartile Range (IQR): The range of the middle 50% of the data: IQR = Q₃ − Q₁.

四分位距 (IQR)：中间 50% 数据的范围：IQR = 上四分位数 Q₃ − 下四分位数 Q₁。

Lower Quartile (Q₁): The value that splits the lowest 25% of ordered data from the rest.

下四分位数 (Q₁)：将排序后数据的最低 25% 与其余部分分开的值。

Upper Quartile (Q₃): The value that splits the highest 25% of ordered data from the rest.

上四分位数 (Q₃)：将排序后数据的最高 25% 与其余部分分开的值。

Semi‑Interquartile Range: Half of the interquartile range, (Q₃ − Q₁) / 2.

半四分位距：四分位距的一半，即 (Q₃ − Q₁) / 2。

Standard Deviation (s): A measure of how spread out the values are around the mean. For a sample:

s = √( Σ(x − x̄)² / (n−1) )

标准差 (s)：衡量数值围绕平均数的离散程度。对于样本：

s = √( Σ(x − x̄)² / (n−1) )

Variance: The square of the standard deviation, s².

方差：标准差的平方，即 s²。

Outlier : An extreme value that lies far away from the rest of the data, often defined as more than 1.5 × IQR below Q₁ or above Q₃.

异常值：远离其余数据的极端值，通常定义为小于 Q₁ − 1.5×IQR 或大于 Q₃ + 1.5×IQR。

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5. Representing Data | 数据表示

Diagrams and charts are used to display data visually, making patterns and comparisons easier to see. Each type of representation has its own rules, and for Eduqas you must be able to construct and interpret them correctly.

图表用于直观展示数据，使模式和比较更易察觉。每种表示形式都有其规则，对于 Eduqas 你必须能够正确地绘制和解读它们。

Bar Chart: Displays categorical data with bars of equal width; the height of each bar represents frequency. Gaps are left between bars.

条形图：用等宽条形显示分类数据；条形高度表示频数。条形之间留有空隙。

Pie Chart: A circular chart divided into sectors, where the angle of each sector is proportional to the frequency of the category.

饼图：分割成扇区的圆形图，每个扇区的角度与类别频数成正比。

Histogram y. The vertical axis shows frequency density: Frequency density = Frequency / Class width.

直方图：用于连续数据或分组数据；每个条形的面积与频数成正比。纵轴表示频率密度：频率密度 = 频数 / 组距。

Frequency Polygon: A line graph formed by joining the midpoints of the tops of histogram bars (or plotted independently).

频数多边形：通过连接直方图条形顶端中点（或独立绘制）形成的折线图。

Cumulative Frequency Diagram: A curve that shows the running total of frequencies. The median and quartiles can be estimated from it.

累积频数图：显示频数累积总和的曲线。可用于估计中位数和四分位数。

Box‑and‑Whisker Plot (Box Plot): A visual summary of a data set showing minimum, Q₁, median, Q₃ and maximum, highlighting spread and outliers.

箱形图（盒须图）：显示最小值、Q₁、中位数、Q₃ 和最大值的数据集视觉摘要，突出离散程度和异常值。

Scatter Graph: Plots pairs of values on two axes to show the relationship between two variables.

散点图：在两个轴上绘制成对数值，以显示两个变量之间的关系。

Stem‑and‑Leaf Diagram: A method of ordering and displaying small data sets while retaining the original values. 'Stem' represents the leading digit(s), 'leaf' the trailing digit.

茎叶图：一种排序和显示小型数据集的方法，同时保留原始值。“茎”代表前导数字，“叶”代表尾随数字。

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6. Probability Basics | 概率基础

Probability measures the chance of an event occurring, expressed as a number between 0 and 1. GCSE Statistics extends basic probability to include relative frequency, expectation and tree diagrams.

概率衡量事件发生的可能性，用 0 到 1 之间的数字表示。GCSE 统计将基本概率扩展到包括相对频率、期望值和树形图。

Experiment: A repeatable process that gives rise to a set of outcomes, e.g. rolling a die.

试验：产生一系列结果的可重复过程，例如掷骰子。

Outcome: A possible result of an experiment.

结果：试验的一个可能结果。

Event: A set of one or more outcomes, e.g. rolling an even number.

事件：一个或多个结果的集合，例如掷出偶数。

Sample Space: The set of all possible outcomes, often listed in a table or diagram.

样本空间：所有可能结果的集合，通常用表格或图表列出。

Theoretical Probability le outcomes / Total number of possible outcomes, assuming all outcomes are equally likely.

理论概率：P(事件) = 有利结果数 / 可能结果总数，假设所有结果等可能。

Experimental Probability (Relative Frequency) ated from an experiment: P(Event) = Number of times event occurs / Total number of trials.

实验概率（相对频率）：通过试验估算：P(事件) = 事件发生次数 / 试验总次数。

Expected Frequency : The number of times an event is predicted to occur: Expected = Probability × Number of trials.

期望频数：预测事件发生的次数：期望频数 = 概率 × 试验次数。

Mutually Exclusive Events: Events that cannot happen at the same time. P(A or B) = P(A) + P(B).

互斥事件：不能同时发生的事件。P(A 或 B) = P(A) + P(B)。

Independent Events ere the outcome of one does not affect the outcome of the other. P(A and B) = P(A) × P(B).

独立事件：一个事件的结果不影响另一个事件的结果。P(A 且 B) = P(A) × P(B)。

Conditional Probability e : The probability of event A happening given that event B has already occurred. Written as P(A|B) = P(A ∩ B) / P(B).

条件概率：在事件 B 已经发生的情况下，事件 A 发生的概率。记作 P(A|B) = P(A ∩ B) / P(B)。

Tree Diagram: A branching diagram that shows all possible outcomes of two or more events and their probabilities.

树形图：显示两个或多个事件所有可能结果及其概率的分支图示。

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7. Correlation and Regression | 相关与回归

Correlation describes the strength and direction of a linear relationship between two variables. Regression goes a step further by finding a line that best fits the data, allowing predictions to be made.

相关描述了两个变量之间线性关系的强度和方向。回归则更进一步，找到一条最能拟合数据的直线，从而进行预测。

Positive Correlation: As one variable increases, the other tends to increase. The scatter points slope upwards.

正相关：一个变量增加，另一个也趋于增加。散点呈向上倾斜。

Negative Correlation: As one variable increases, the other tends to decrease. The scatter points slope downwards.

负相关：一个变量增加，另一个趋于减少。散点呈向下倾斜。

Zero Correlation: No clear linear pattern between the variables.

零相关：变量之间没有明显的线性模式。

Correlation Coefficient (r) orrelation. r = +1 perfect positive, r = −1 perfect negative, r = 0 no linear correlation.

相关系数 (r)：介于 −1 和 +1 之间的数字，衡量线性相关的强度。r = +1 完全正相关，r = −1 完全负相关，r = 0 无线性相关。

Line of Best Fit: A straight line drawn through a scatter graph to represent the trend. It should have roughly equal numbers of points above and below it.

最佳拟合线：穿过散点图的一条直线，代表总体趋势。线上下的点数量应大致相等。

Interpolation: Estimating a value within the range of the given data using the line of best fit.

内插：利用最佳拟合线在已知数据范围内估计一个值。

Extrapolation: Estimating a value outside the range of the given data. This can be unreliable.

外推：在已知数据范围之外估计一个值，可能不可靠。

Causal Relationship: When a change in one variable directly causes a change in another. Correlation does not imply causation.

因果关系：一个变量的变化直接导致另一个变量变化。相关不意味着因果。

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8. Time Series | 时间序列

A time series records data points at successive time intervals. Analysing time series involves identifying trends and seasonal patterns, and calculating moving averages to smooth out fluctuations.

时间序列记录了连续时间间隔上的数据点。分析时间序列包括识别趋势和季节模式，以及计算移动平均来平滑波动。

Time Series Plot: A line graph with time on the horizontal axis and the variable of interest on the vertical axis.

时间序列图：以时间为横轴、关注变量为纵轴的折线图。

Trend: The long‑term movement in the

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