📚 Year 12 WJEC Statistics: Quick Vocabulary & Terminology Guide | Year 12 WJEC 统计：词汇术语速记指南
Mastering statistical vocabulary is the first step to success in Year 12 WJEC Statistics. This guide provides clear English definitions with Chinese translations for all the key terms you will encounter, from data types to hypothesis testing. Use it to build your bilingual fluency and deepen your understanding of statistical concepts.
掌握统计词汇是 Year 12 WJEC 统计学取得成功的第一步。本指南为你提供清晰的中英对照定义，涵盖从数据类型到假设检验的所有关键术语。利用它来提升你的双语流畅度，并加深对统计概念的理解。
1. Types of Data | 数据类型
In statistics, data can be classified in several ways. Understanding the type of data you are working with determines which statistical techniques are appropriate.
在统计学中，数据可以用多种方式分类。了解你正在处理的数据类型，决定了哪些统计方法是合适的。
Qualitative (Categorical) Data: Non-numerical data that can be sorted into categories, such as eye colour or favourite sport. Qualitative data can be nominal or ordinal.
定性数据（分类数据）：可以归入不同类别的非数值数据，例如眼睛颜色或最喜爱的运动。定性数据可以是名义的或有序的。
Quantitative Data: Numerical data that represent quantities. This type can be further divided into discrete and continuous data.
定量数据：表示数量的数值数据。这种类型可进一步分为离散数据和连续数据。
Discrete Data: Quantitative data that can only take certain, distinct values (often integers), such as the number of students in a class. Discrete data usually arise from counting.
离散数据：只能取特定、不同值（通常是整数）的定量数据，例如班级中的学生人数。离散数据通常来自计数。
Continuous Data: Quantitative data that can take any value within a given range, such as height or weight. Continuous data arise from measuring.
连续数据：可以在给定范围内取任何值的定量数据，例如身高或体重。连续数据来自测量。
Nominal Data: Qualitative data where categories have no natural order (e.g., blood type, gender). The only calculation possible is counting the frequency in each category.
名义数据：类别没有自然顺序的定性数据（例如血型、性别）。唯一可能的计算是统计每个类别的频数。
Ordinal Data: Qualitative data with a clear order or ranking, but the differences between ranks are not necessarily equal (e.g., survey ratings: poor, average, good).
有序数据：具有明确顺序或等级的定性数据，但等级之间的差异不一定相等（例如调查评级：差、一般、好）。
2. Sampling Methods | 抽样方法
Sampling is the process of selecting a subset of individuals from a population to estimate characteristics of the whole group. The design of a sample affects the validity of conclusions.
抽样是从总体中选择一部分个体的过程，用以估计整个群体的特征。样本的设计会影响结论的有效性。
Population: The entire set of individuals or items that are of interest for a statistical study.
总体：某项统计研究感兴趣的全部个体或项目。
Sample: A subset of the population selected for the actual investigation.
样本：从总体中选出来进行实际调查的子集。
Census: A study that attempts to collect data from every member of the population. It is often impractical or expensive.
普查：试图从总体的每个成员收集数据的研究。通常不切实际或成本高昂。
Simple Random Sample (SRS): A sample where every member of the population has an equal chance of being selected, and all combinations are equally likely. This reduces bias.
简单随机样本：总体中的每个成员被选中的机会均等，且所有组合概率相同的样本。这可以减少偏差。
Stratified Sampling: The population is divided into distinct subgroups (strata), and a random sample is taken from each stratum in proportion to its size. This guarantees representation.
分层抽样：将总体分成不同的子组（层），然后按各层大小比例从每层中随机抽取样本。这能确保代表性。
Systematic Sampling: Every k-th individual is selected from a list after a random start. Convenient but may introduce periodicity bias.
系统抽样：随机起点之后，从名单中每隔 k 个个体选取一个。方便可行，但可能引入周期性偏差。
Cluster Sampling: The population is divided into clusters, and a random sample of clusters is chosen. All individuals within selected clusters are included. Useful when population is geographically spread.
整群抽样：将总体分成群，随机抽取若干群，选中群内的所有个体都包含在内。当总体地理分布广泛时很有用。
Quota Sampling: An interviewer selects a fixed number of subjects matching certain profiles. It is non-random and can lead to selection bias.
配额抽样：采访者选取固定数量的符合某些特征的个体。这是非随机的，可能导致选择偏差。
Bias: A systematic error that causes results to deviate from the true population parameter. Biased samples over- or under-represent certain groups.
偏差：导致结果偏离真实总体参数的系统性误差。有偏样本会高估或低估某些群体。
3. Measures of Central Tendency | 集中趋势的度量
Measures of central tendency summarise a data set with a single value representing the centre or typical value.
集中趋势的度量用一个单一数值概括数据集，表示中心点或典型值。
Mean: The arithmetic average, calculated as the sum of all data values divided by the number of observations. It is sensitive to outliers. Notation: x̄ for sample, μ for population.
均值：算术平均数，等于所有数据值之和除以观测数。对异常值敏感。符号：样本用 x̄，总体用 μ。
Median: The middle value when the data are arranged in order. For an even number of observations, it is the average of the two middle values. It is robust to outliers.
中位数：将数据按顺序排列后位于中间的值。若有偶数个观测值，则取中间两个值的平均数。对异常值稳健。
Mode: The value that appears most frequently. A data set may have one mode (unimodal), two modes (bimodal), or more. It is the only measure suitable for nominal data.
众数：出现频率最高的值。一个数据集可能有一个众数（单峰）、两个众数（双峰）或更多。是唯一适用于名义数据的度量。
Weighted Mean: A mean where each data point contributes a different weight, reflecting its importance. Used in index numbers and when combining group means.
加权均值：每个数据点被赋予不同权重的均值，反映其重要性。用于指数以及合并组均值时。
4. Measures of Dispersion | 离散程度的度量
Dispersion measures the spread or variability of a data set. Together with a measure of central tendency, it gives a more complete picture of the data.
离散度衡量数据集的散布或变异性。配合集中趋势度量，可以更全面地描述数据。
Range: The difference between the largest and smallest values. It is simple 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 range of the middle 50% he data: IQR = Q₃ - Q₁. It is not affected by outliers and is used to construct box plots.
四分位距 (IQR)：中间 50% 数据的范围：IQR = Q₃ - Q₁。不受异常值影响，用于构建箱线图。
Lower Quartile (Q₁): The median of the lower half of the data; 25% of observations lie below this value.
下四分位数 (Q₁)：数据下半部分的中位数；25% 的观测值低于此数。
Upper Quartile (Q₃): The median of the upper half; 75% of observations lie below this value.
上四分位数 (Q₃)：数据上半部分的中位数；75% 的观测值低于此数。
Variance : The average of the squared deviations from the mean. It measures total spread. Sample variance: s² = Σ(x - x̄)² / (n-1). Population variance: σ².
方差：各数据与均值之差平方的平均数。衡量总离散度。样本方差：s² = Σ(x - x̄)² / (n-1)。总体方差：σ²。
Standard Deviation: The square root of the variance. It is expressed in the same units as the original data. Sample standard deviation: s; population: σ.
标准差：方差的平方根。与原始数据单位相同。样本标准差：s；总体：σ。
5. Graphical Representations | 图形表示
Statistical diagrams help to visualise distributions, spot patterns, and communicate findings efficiently.
统计图表有助于可视化分布、发现规律并有效地传达结果。
Bar Chart: Uses vertical or horizontal bars to represent frequencies or percentages of categorical data. Gaps between bars indicate discrete categories.
条形图：用垂直或水平条表示分类数据的频数或百分比。条与条之间的间隙表示离散类别。
Histogram: A diagram for continuous data where the area of each bar is proportional to the frequency. Bar width corresponds to class width, so frequency density is used on the vertical axis.
直方图：用于连续数据的图示，每个条的面积与频数成比例。条宽对应组距，因此纵轴使用频率密度。
Frequency Polygon: A line graph formed by joining the midpoints of histogram tops with straight lines. Useful for comparing distributions.
频数多边形：用直线连接直方图顶部中点而成的折线图。适用于比较分布。
Cumulative Frequency Curve (Ogive): A graph plotting cumulative frequency against the upper class boundary. It is used to estimate medians, quartiles, and percentiles.
累积频数曲线（拱形图）：标绘累积频数与组上界的图形。用于估算中位数、四分位数和百分位数。
Box and Whisker Plot (Box Plot): Displays the minimum, Q₁, median, Q₃, and maximum. Outliers are marked individually. It clearly shows the spread and skewness of the data.
箱线图：显示最小值、Q₁、中位数、Q₃ 和最大值。异常值单独标注。能清晰显示数据的散布和偏态。
Scatter Diagram: A graph of paired numerical data showing the relationship between two variables. The pattern suggests correlation and can guide regression.
散点图：成对数值数据的图形，显示两个变量之间的关系。点的分布形态提示相关性并可指导回归。
Stem-and-Leaf Diagram: A semi-graphical way of showing the shape of a distribution while retaining the original data values. The stem represents the leading digit(s), and the leaf is the final digit.
茎叶图：一种半图形化方式，展示分布形态并保留原始数据值。茎代表前导数字，叶是最后一位数字。
6. Probability Concepts and Rules | 概率概念与法则
Probability quantifies uncertainty. Building a solid foundation in its terminology is essential for tackling random variables and distributions.
概率量化不确定性。在术语上打下坚实基础对应对随机变量和分布至关重要。
Experiment: A repeatable process that produces a set of outcomes, such as rolling a die.
试验：一个可重复的过程，会产生一组结果，例如掷一个骰子。
Outcome: A single possible result of an experiment.
结果：一次试验可能出现的单个结果。
Sample Space (S): The set of all possible outcomes of an experiment.
样本空间 (S)：一次试验所有可能结果的集合。
Event: A subset of the sample space. An event is a collection of one or more outcomes.
事件：样本空间的子集。事件由一个或多个结果组成。
Mutually Exclusive Events: Two events that cannot happen at the same time. P(A ∩ B) = 0.
互斥事件：不可能同时发生的两个事件。P(A ∩ B) = 0。
Independent Events: Two events where the occurrence of one does not affect the probability of the other. P(A ∩ B) = P(A) × P(B).
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