📚 Vocabulary Terminology Quick-Reference Guide | 词汇术语速记指南
Welcome to this WJEC GCSE Statistics vocabulary quick-reference guide for Year 10. Mastering the key terms is essential for understanding data, probability, and statistical methods. This bilingual guide pairs each definition in English and Chinese to help you memorise the terminology efficiently. Use it alongside your revision to boost your confidence in the exam.
欢迎使用这份针对 Year 10 WJEC GCSE 统计的词汇速记指南。掌握关键术语对于理解数据、概率和统计方法至关重要。本双语指南为每个定义提供中英文对照，帮助您高效记忆术语。结合使用，提升考试信心。
1. Data Types | 数据类型
Qualitative (categorical) data: non-numerical information, such as eye colour or car make.
定性（分类）数据：非数值信息，例如眼睛颜色或汽车品牌。
Quantitative discrete data: numerical data that can only take certain values, often counted in whole numbers, like number of students in a class.
定量离散数据：只能取特定值的数值数据，通常以整数计数，如班级学生人数。
Quantitative continuous data: numerical data that can take any value within a range, usually measured, like height or time.
定量连续数据：可以在一个范围内取任何值的数值数据，通常通过测量得到，如身高或时间。
2. Population and Sample | 总体与样本
Population: the entire set of individuals or items of interest.
总体：所关注的全部个体或项目组成的集合。
Sample: a subset of the population used to make inferences about the whole.
样本：总体的一个子集，用于推断总体特征。
Census: a survey that collects data from every member of the population.
普查：从总体每一个成员收集数据的调查。
3. Sampling Methods | 抽样方法
Random sampling: every member of the population has an equal chance of being selected; avoids bias.
随机抽样：总体每个成员被选中的机会均等；可避免偏差。
Stratified sampling: the population is divided into groups (strata) and a random sample is taken from each group in proportion to its size.
分层抽样：将总体划分为若干层，然后按各层规模比例随机抽取样本。
Systematic sampling: selecting every nth member from a list after a random starting point.
系统抽样：从名单中随机确定起点后，每隔一定间隔选取一个成员。
Convenience sampling: choosing individuals who are easiest to reach; likely to be biased.
便利抽样：选择最容易接触的个体；容易产生偏差。
4. Frequency Distributions | 频数分布
Frequency: the number of times a data value or class occurs.
频数：某个数据值或类别出现的次数。
Frequency distribution table: a table listing data values/classes and their frequencies.
频数分布表：列出数据值/组别及其频数的表格。
Cumulative frequency: a running total of frequencies up to a certain class boundary.
累积频数：累计至某个组界的频数总和。
Relative frequency: frequency divided by total number of observations; an estimate of probability.
相对频数：频数除以观测总数；可用于估计概率。
5. Averages and Spread | 平均数与离散度
Mean (x̄): the sum of all values divided by the number of values. Formula: x̄ = Σx / n
平均数（x̄）：所有数值之和除以数值的个数。公式：x̄ = Σx / n
Median: the middle value when data are ordered; for even number, average of the two middle values.
中位数：数据排序后位于中间的数值；数据个数为偶数时取中间两个数的平均值。
Mode: the value that appears most frequently.
众数：出现次数最多的数值。
Range: the difference between maximum and minimum values.
极差：最大值与最小值的差值。
Interquartile range (IQR): Q₃ – Q₁; the range of the middle 50% of data.
四分位距 (IQR)：Q₃ – Q₁；中间 50% 数据的分布范围。
Standard deviation (s): a measure of how spread out the data are from the mean; a smaller value indicates less variability. For a sample, s = √[ Σ(x – x̄)² / (n – 1) ]. The WJEC specification also covers the population standard deviation with divisor n.
标准差（s）：衡量数据相对于平均值的离散程度；数值越小表示变异性越小。对于样本，s = √[ Σ(x – x̄)² / (n – 1) ]。WJEC 考试也涉及除以 n 的总体标准差。
6. Box Plots and IQR | 箱线图与四分位距
Box plot (box-and-whisker plot): displays the minimum, lower quartile (Q₁), median (Q₂), upper quartile (Q₃), and maximum.
箱线图（箱须图）：显示最小值、下四分位数（Q₁）、中位数（Q₂）、上四分位数（Q₃）和最大值。
Outlier: a value that lies more than 1.5 × IQR below Q₁ or above Q₃.
异常值：低于 Q₁ – 1.5×IQR 或高于 Q₃ + 1.5×IQR 的数值。
IQR: Q₃ – Q₁, a resistant measure of spread.
四分位距：Q₃ – Q₁，一种抗异常值的离散度度量。
7. Charts and Diagrams | 图表与图示
Histogram: used for grouped continuous data; area of each bar is proportional to frequency; frequency density = frequency ÷ class width.
直方图：用于分组连续数据；每个长方形的面积与频数成正比；频率密度 = 频数 ÷ 组距。
Frequency polygon: a line graph joining the midpoints of the tops of histogram bars.
频数多边形：连接直方图各长方形顶部中点的折线图。
Stem-and-leaf diagram: shows raw data and shape; stem is leading digit(s), leaf is trailing digit.
茎叶图：既展示原始数据又呈现分布形状；茎为首位数字，叶为末位数字。
Pie chart: a circular chart where sectors represent categories proportionally (angle = (frequency/total) × 360°).
饼图：用扇形表示各类别占比的圆形图（角度 =（频数/总数）× 360°）。
8. Probability Basics | 概率基础
Experiment: a repeatable process with observable outcomes.
试验：可重复进行并有可观测结果的过程。
Outcome: a possible result of an experiment.
结果：试验可能的结局。
Event: a set of one or more outcomes.
事件：一个或多个结果的集合。
Probability scale: from 0 (impossible) to 1 (certain). Probability = (number of favourable outcomes) / (total number of equally likely outcomes).
概率标度：从 0（不可能）到 1（必然）。概率 =（有利结果数）/（等可能结果总数）。
Expected frequency: expected number of times an event occurs = probability × number of trials.
期望频数：事件预期发生的次数 = 概率 × 试验次数。
9. Independent and Mutually Exclusive Events | 独立事件与互斥事件
Mutually exclusive events: cannot happen at the same time; P(A or B) = P(A) + P(B).
互斥事件：不可能同时发生的事件；P(A 或 B) = P(A) + P(B)。
Independent events: the outcome of one event does not affect the probability 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发生的概率；P(A 且 B) = P(A) × P(B)。
Tree diagrams: help to calculate probabilities of combined independent events by multiplying along branches.
树形图：通过沿分支相乘来计算组合独立事件的概率。
Venn diagrams: show sets and their intersections; useful for ‘AND’ and ‘OR’ probability.
韦恩图：展示集合及其交集；适用于“且”和“或”的概率。
10. Scatter Graphs and Correlation | 散点图与相关性
Scatter graph: a plot of bivariate data; each point represents a pair of values (x, y).
散点图：双变量数据的图形；每个点代表一对数值 (x, y)。
Correlation: describes the relationship between two variables – positive (as x increases, y tends to increase), negative (as x increases, y tends to decrease), or none.
相关性：描述两个变量之间的关系——正相关（x 增大时 y 趋于增大）、负相关（x 增大时 y 趋于减小）或无相关。
Line of best fit: a straight line drawn through the scatter graph to show the trend; can be used to estimate values (interpolation within the range; extrapolation outside the range, which is less reliable).
最佳拟合线：穿过散点图的一条直线，显示趋势；可用于估计数值（内插法在数据范围内，外推法在范围外，可靠性较低）。
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