📚 Year 11 AQA Statistics: Quick Glossary Guide | Year 11 AQA 统计：术语速记指南
Mastering statistical terminology is the first step towards excelling in your AQA Statistics exam. This guide presents key terms with clear definitions, paired with Chinese translations, to help you build a solid bilingual vocabulary. Understanding these terms will allow you to interpret questions accurately and convey your reasoning effectively.
掌握统计术语是你在AQA统计考试中取得好成绩的第一步。本指南提供了关键术语的清晰定义，并附上中文翻译，帮助你建立扎实的双语词汇。理解这些术语将使你能够准确解读题目，并有效地表达你的推理。
1. Types of Data | 数据类型
Data is the foundation of statistics. Recognising whether you have qualitative or quantitative, discrete or continuous data determines which diagrams and calculations are appropriate.
数据是统计学的基石。识别你处理的是定性还是定量、离散还是连续数据，决定了哪些图表和计算方法是合适的。
Qualitative data: Non-numerical data that describes qualities or categories, such as eye colour, type of car, or favourite film. It is often called categorical data.
定性数据：描述质量或类别的非数值数据，如眼睛颜色、汽车类型或最喜欢的电影。它常被称为分类数据。
Quantitative data: Numerical data that can be measured or counted, such as height, test scores, or number of pets. It can be further divided into discrete and continuous.
定量数据：可以测量或计数的数值数据，如身高、测试分数或宠物数量。它可进一步分为离散型和连续型。
Discrete data: Quantitative data that can only take specific, separate values, often whole numbers. Examples: number of students in a class (you cannot have 28.5 students).
离散数据：只能取特定、分离数值的定量数据，通常是整数。例如：一个班级的学生人数（不可能有 28.5 名学生）。
Continuous data: Quantitative data that can take any value within a given range and is measured, not counted. Examples: mass, time, temperature.
连续数据：可在给定范围内取任何值的定量数据，是测量而非计数得到的。例如：质量、时间、温度。
Primary data: Data collected directly by the researcher for a specific purpose, such as a survey you conduct yourself.
原始数据：由研究人员为特定目的直接收集的数据，例如你自己进行的问卷调查。
Secondary data: Data that has already been collected by someone else and is being reused, such as government statistics or internet databases.
二手数据：已由他人收集并被再次使用的数据，如政府统计数据或网络数据库。
2. Sampling Techniques | 抽样技术
A sample is a subset of the population used to draw conclusions. The method of sampling affects the reliability of those conclusions.
样本是用于得出结论的总体子集。抽样方法会影响这些结论的可靠性。
Population: The entire group of individuals or items that you are interested in studying.
总体：你有兴趣研究的全部个体或项目组成的集合。
Sample: A smaller selection taken from the population that is used to represent it.
样本：从总体中选出的、用于代表总体的较小部分。
Sampling frame: A list of all the members of the population from which a sample can be drawn, e.g. an electoral register.
抽样框：一份列出总体所有成员的清单，可从中抽取样本，例如选民登记册。
Random sample: A sample where every member of the population has an equal chance of being selected, reducing bias.
随机样本：总体中每个成员都有均等机会被选中的样本，可减少偏差。
Stratified sampling: The population is divided into groups (strata) based on a characteristic, and a random sample is taken from each group in proportion to its size.
分层抽样：将总体按某种特征分成若干层，然后在每一层中按比例随机抽取样本。
Systematic sampling: Every k-th item is chosen from the sampling frame after a random start, e.g. selecting every 10th person on a list.
系统抽样：在随机起点后，从抽样框中每隔 k 个选取一个样本，例如从名单上每第 10 个人中选取。
Quota sampling: Interviewers are given a set number of people from different groups to find, without random selection. It is non-probability sampling.
配额抽样：访问员被要求寻找不同群体中特定数量的受访者，不做随机选择，属于非概率抽样。
Opportunity sampling: A sample taken from people who are available at the time of the study and fit the criteria, often the most convenient option.
便利抽样：在研究时从可接触且符合条件的人群中抽取样本，通常是最方便的选择。
3. Measures of Central Tendency | 集中趋势度量
These measures describe the centre or typical value of a data set. Each has strengths and limitations depending on the data distribution.
这些度量描述数据集的中心或典型值。根据数据分布，每种度量都有其优点和局限性。
Mean: The arithmetic average, found by adding all data values and dividing by the number of values. It uses all data but is sensitive to outliers.
均值：算术平均数，将所有数据值相加后除以数据个数。它利用了所有数据，但对异常值敏感。
Median: The middle value when the data are arranged in order. Half the values lie below and half above. Not affected by outliers.
中位数：将数据按顺序排列后位于中间的值。一半数值在其下，一半在其上，不受异常值影响。
Mode: The value that occurs most frequently in a data set. A data set can have one mode, more than one, or no mode at all.
众数：数据集中出现频率最高的值。数据可以有一个众数、多个众数或完全没有众数。
Weighted mean: An average where some values contribute more than others, often used in index numbers or when combining averages.
加权平均数：某些值的贡献更大的平均值，常用于指数计算或合并平均数时。
4. Measures of Dispersion | 离散程度度量
Dispersion measures describe how spread out the data are. They indicate the consistency and reliability of the data set.
离散程度度量描述数据的分散程度，反映数据集的稳定性和可靠性。
Range: The difference between the largest and smallest values. Easy to calculate but affected by extreme values.
极差：最大值与最小值之差。计算简单，但受极端值影响。
Interquartile range (IQR): The difference between the upper quartile (Q3) and the lower quartile (Q1), representing the middle 50% of the data. It is resistant to outliers.
四分位距 (IQR)：上四分位数 (Q3) 与下四分位数 (Q1) 的差值，代表中间 50% 的数据。它不受异常值影响。
Variance: A measure of the average squared distance of each data point from the mean. It forms the basis for standard deviation.
方差：每个数据点与均值之差的平方的平均值，是标准差的基础。
Standard deviation: The square root of the variance, measuring the typical distance from the mean. A larger standard deviation implies more spread.
标准差：方差的平方根，测量数据与均值的典型距离。标准差越大，数据越分散。
Outlier: e from the rest of the data. Often identified using 1.5 × IQR rule or standard deviations.
异常值：与其他数据相距异常远的数据值。通常用 1.5 × 四分位距法则或标准差来识别。
5. Graphical Representations | 图形表示
Visual summaries of data reveal patterns, trends, and comparisons. Choosing the right graph depends on the type of data and the story you want to tell.
数据的可视化摘要揭示模式、趋势和对比。选择合适的图表取决于数据类型和你想传达的信息。
Bar chart: Used for categorical or discrete data, with bars separated by gaps. The height or length of each bar shows the frequency.
条形图：用于分类或离散数据，条形之间有间隔。每个条形的高度或长度表示频数。
Pie chart: A circular chart divided into sectors, each representing a proportion of a whole. Best for showing percentages of categorical data.
饼图：将圆分成多个扇形区域的图表，每个扇形代表整体的一个比例。最适合展示分类数据的百分比。
Histogram: Used for continuous data where the area of each bar represents frequency. Bars touch to show the continuous nature, and class widths can vary.
直方图：用于连续数据，每个条形的面积代表频数。条形相连以体现连续性，组距可以不等。
Box plot (box-and-whisker plot): Displays the minimum, lower quartile, median, upper quartile, and maximum. Useful for comparing distributions and spotting skewness.
箱线图：显示最小值、下四分位数、中位数、上四分位数和最大值。适用于比较分布和发现偏态。
Cumulative frequency diagram: A curve showing the running total of frequencies. The median and quartiles can be estimated from the graph.
累积频数图：显示频数累积总数的曲线，可从图中估算中位数和四分位数。
Scatter diagram: A graph of plotted points showing the relationship between two variables. It is the first step in correlation analysis.
散点图：由绘制的点构成的图，展示两个变量之间的关系。这是相关分析的第一步。
6. Probability Essentials | 概率要点
Probability quantifies how likely an event is to happen. It is expressed as a number from 0 (impossible) to 1 (certain).
概率量化事件发生的可能性，用 0（不可能）到 1（必然）之间的一个数字表示。
Experiment: A repeatable process that gives rise to a set of outcomes, such as tossing a coin or rolling a dice.
试验：可重复进行、会产生一系列结果的过程，如抛硬币或掷骰子。
Outcome: A possible result of an experiment, e.g. getting a '4' on a dice.
结果：试验的一个可能结果，如在骰子上掷出 '4'。
Event: A set of one or more outcomes. For example, 'rolling an even number' is an event containing outcomes 2, 4, and 6.
事件：一个或多个结果的集合。例如，“掷出偶数”是一个事件，包含结果 2、4 和 6。
Sample space: The set of all possible outcomes of an experiment. It is often listed systematically or shown in a diagram.
样本空间：一项试验所有可能结果的集合，通常系统地列出或用图表表示。
Theoretical probability: The likelihood of an event based on equally likely outcomes, calculated as (number of favourable outcomes) / (total number of outcomes).
理论概率：基于等可能结果的事件可能性，计算公式为（有利结果数）/（总结果数）。
Experimental probability (relative frequency): An estimate of probability based on the results of an actual experiment or past data.
实验概率（相对频率）：基于实际实验结果或历史数据对概率的估计。
Mutually exclusive events: vents that cannot happen at the same time. For mutually exclusive A and B, P(A and B) = 0.
互斥事件：不能同时发生的事件。若 A 与 B 互斥，则 P(A 且 B) = 0。
Independent events: : Two events where the occurrence of one does not affect the probability of the other. P(A and B) = P(A) × P(B) if independent.
独立事件：一个事件的发生不影响另一个事件发生概率的两个事件。若独立，P(A 且 B) = P(A) × P(B)。
Tree diagram: A branching diagram used to list all possible outcomes of a sequence of events, with probabilities written on the branches.
树形图：用于列出一系列事件所有可能结果的分支图，分支上写有概率。
7. Correlation and Regression | 相关与回归
Correlation describes the strength and direction of a linear relationship between two variables. Regression gives a line of best fit to make predictions.
相关描述两个变量之间线性关系的强度和方向。回归给出最佳拟合线用于预测。
Correlation: A measure of how two variables change together. It does not imply one variable causes the other to change.
相关：两个变量一起变化程度的度量，它并不意味着一个变量导致另一个变量变化。
Positive correlation: As one variable increases, the other tends to increase. The scatter points slope upwards.
正相关：当一个变量增大时，另一个变量也倾向于增大的关系。散点呈上升趋势。
Negative correlation: As one variable increases, the other tends to decrease. The scatter points slope downwards.
负相关：当一个变量增大时，另一个变量倾向于减小的关系。散点呈下降趋势。
Correlation coefficient (r): A value between -1 and 1 that measures the strength and direction of linear correlation. Values close to 1 or -1 indicate strong correlation; values near 0 indicate weak correlation.
相关系数 (r)：介于 -1 和 1 之间的值，衡量线性相关的强度和方向。接近 1 或 -1 表示强相关，接近 0 表示弱相关。
Line of best fit: A straight line drawn through a scatter diagram that best represents the data points. It can be used to estimate unknown values.
最佳拟合线：穿过散点图、最能代表数据点的一条直线，可用于估计未知值。
Interpolation: Estimating a value within the range of the given data, using the line of best fit. It is generally reliable.
内插：利用最佳拟合线在已知数据范围内估计数值。通常较为可靠。
Extrapolation: Estimating a value outside the range of the given data. It is less reliable because the established trend may not continue.
外推：在已知数据范围之外估计数值。由于已建立的趋势可能不会延续，可靠性较低。
Causation: A direct link where a change in one variable directly produces a change in another. Correlation does not automatically mean causation.
因果关系：一个变量的变化直接导致另一个变量变化的关系。相关并不自动意味着因果关系。
8. Index Numbers | 指数
Index numbers simplify the comparison of prices or quantities over time, often setting a base year to 100 to measure percentage changes.
指数简化了价格或数量随时间变化的比较，通常将基年设为 100 来衡量百分比变化。
Index number: A numerical value showing the relative change in a variable, such as price, compared to a base value. It shows proportional change.
指数：显示变量（如价格）相对于基值的相对变化的数值，反映比例变化。
Base year: The reference year, commonly assigned an index value of 100, with which all other years are compared.
基年：被指定为参照点的年份，通常赋予指数值 100，其他所有年份与之比较。
Price relative: A basic index giving the ratio of the current price to the base price, usually multiplied by 100.
价比：当前价格与基价的比率，通常乘以 100 来表示的基础指数。
Weighted index: An index that combines different items by giving greater importance (weight) to those with larger impact, such as using quantities sold.
加权指数：通过给予影响更大的项目更大重要性（权重）来综合不同项目，例如使用销售量作为权重。
Consumer Price Index (CPI): An official measure of inflation in the UK, tracking changes in the cost of a fixed basket of goods and services over time.
消费者价格指数 (CPI)：英国官方的通货膨胀衡量指标，追踪一篮子固定商品和服务成本随时间的变化。
9. Time Series and Forecasting | 时间序列与预测
Time series data is recorded over regular intervals. Analysing the components helps identify patterns and make predictions.
时间序列数据按固定时间间隔记录。分析其组成部分有助于识别模式并进行预测。
Time series: A sequence of data points collected or recorded at successive equally spaced points in time, e.g. monthly sales figures.
时间序列：在连续、等间隔的时间点上收集或记录的数据点序列，例如月度销售额。
Trend: The long-term underlying movement in a time series, ignoring short-term fluctuations. It shows the general direction.
趋势：时间序列中忽略短期波动的长期基本走向，显示总体方向。
Seasonal variation: A regular and predictable pattern that repeats over a fixed period, such as higher ice cream sales every summer.
季节变动：在固定周期内重复出现的规律性、可预测的模式，例如每年夏季冰淇淋销量上升。
Moving average: A series of averages calculated from successive fixed-sized subsets of the data, used to smooth out short-term fluctuations and highlight the trend.
移动平均：通过连续固定大小的数据子集计算出一系列平均值，用于平滑短期波动并凸显趋势。
Forecast: A prediction of future values of a time series, based on the estimated trend and seasonal adjustments.
预测：基于估计的趋势和季节调整，对时间序列未来值的推测。
10. Standardised Scores | 标准化分数
Standardised scores describe a data value's position relative to the mean and standard deviation, making it possible to compare values from different distributions.
标准化分数描述一个数据值相对于均值和标准差的位置，使得比较不同分布中的数值成为可能。
Standardised score (z-score): Tells you how many standard deviations a data value is above or below the mean. Calculated as (value - mean) / standard deviation.
标准化分数（z-分数）：表示一个数据值高于或低于均值多少个标准差。计算公式为（数值 - 均值）/ 标准差。
Mean as reference: A z-score of 0 means the data value is exactly at the mean of the distribution.
以均值为参照：z-分数为 0 表示该数据值恰好位于分布的均值处。
Positive z-score: The value is above the mean. The larger the positive number, the further above the mean it lies.
正 z-分数：数值在均值之上。正数越大，表示高于均值的程度越大。
Negative z-score: The value is below the mean. A more negative number indicates the value is further below the mean.
负 z-分数：数值在均值之下。负数越小（绝对值越大），表示低于均值的程度越大。
Comparison: Standardising allows you to compare, for example, a student's performance in two different subjects with different means and standard deviations.
比较：通过标准化，你可以比较同一学生在具有不同均值和标准差的两门科目中的表现。
Published by TutorHao | Statistics Revision Series | aleveler.com
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