📚 IGCSE WJEC Statistics: Key Terms Quick Memorisation Guide | IGCSE WJEC 统计：词汇术语速记指南
Mastering the vocabulary of Statistics is half the battle when preparing for your IGCSE WJEC exam. Whether you are interpreting a question about "bivariate data" or describing a "negatively skewed distribution", precise terminology can earn you marks in both calculations and written explanations. This quick guide pairs every key term with a simple definition, a memory hook, and its exact Chinese equivalent, so you can revise effectively and avoid confusion on exam day.
掌握统计学术语是应对 IGCSE WJEC 考试的关键一环。无论是解读“双变量数据”还是描述“负偏态分布”，准确的术语能够帮你在计算和文字解释中双双得分。这篇速记指南为每个核心术语配上了简明定义、记忆窍门以及准确的中文对应词，帮助你高效复习，考试时不再混淆。
1. Data Types and Classification | 数据类型与分类
Qualitative data is non-numerical, descriptive information that categorises attributes or qualities. Examples include hair colour, gender, or the brand of a car. Remember: "Quality" starts with "Quali-". In WJEC papers, you may also see the term "categorical data" used interchangeably. A quick memory trick: qualitative data asks "what type?", not "how many?".
定性数据是非数值的描述性信息，用于对属性或特征进行分类，例如头发颜色、性别或汽车品牌。记住：“定性”的“性”指性质，不是数字。在 WJEC 试题中，它也可能被称为“分类数据”。记忆诀窍：定性数据问的是“哪一种？”，而不是“多少个？”。
Quantitative data is numerical and can be counted or measured. It splits into discrete data (exact countable values, such as number of pets, shoe size) and continuous data (values that can take any number within a range, like height, time, temperature). Think of discrete as "distinct dots" on a number line, while continuous fills the whole interval. Quick link: "Discrete" and "distinct" share the same Latin root.
定量数据是数值型数据，可以被计数或测量。它分为离散数据（精确可数的值，如宠物数量、鞋码）和连续数据（在区间内可任意取值的量，如身高、时间、温度）。想象数轴上离散数据是孤立的点，连续数据填满整个区间。记忆：离散和“单独”关联，连续则意味着“连绵不断”。
Nominal data is a type of qualitative data where labels have no inherent order (e.g., bus, train, car). Ordinal data has ordered categories but no consistent scale between ranks (e.g., satisfaction ratings: poor, fair, good). A quick reminder: "Nominal" relates to "name", while "Ordinal" implies "order".
名义数据是一种无序的定性数据，标签没有内在顺序（如公交车、火车、小汽车）。顺序数据的类别有次序，但等级之间的差距并不一致（如满意度评级：差、一般、好）。记忆窍门："Nominal"与“name”（名称）同源，"Ordinal"包含“order”（顺序）的含义。
2. Sampling Terminology | 抽样术语
The population is the entire set of individuals or items you are interested in studying. The sample is a smaller group selected from the population. To remember: "Population" starts with "Pop" like "Popular" — it includes everybody. A good sample should be representative of the population, meaning it mirrors its key characteristics.
总体是你想研究的全部个体或项目的集合。样本是从总体中选出的一小部分。记忆方法："Population" 像 "popular"，包含所有人。一个好的样本应当具有代表性，即能反映总体的关键特征。
A simple random sample gives every member of the population an equal chance of selection, often using a random number generator. Stratified sampling divides the population into distinct groups (strata) and takes a proportional random sample from each. Think of strata as "layers" — like slicing a cake to get a fair share of each flavour. Systematic sampling selects every kth member from a list. The starting point should be random. The formula for the sampling interval k is population size ÷ sample size.
简单随机抽样让总体中每个成员都有相等的被选中机会，通常借助随机数生成器。分层抽样将总体分成不同的层，然后从每层中按比例随机抽取样本。把“层”想象成蛋糕的不同口味层，以确保每个口味都有代表。系统抽样从名单中每隔k个选一个样本，起始点需随机。抽样间距k的公式为：总体大小 ÷ 样本大小。
Bias in sampling occurs when the method consistently over- or under-represents some part of the population. For instance, surveying only people at a bus stop will bias the sample towards public transport users. To avoid bias, use randomisation. The phrase "bias bounces results away from truth" can help you recall its negative impact.
抽样中的偏差（偏倚）是指方法系统性地高估或低估了总体的某一部分。例如，只在公交站调查会使样本偏向公共交通使用者。要避免偏差，就需要随机化。记住“偏差让结果偏离真相”，就能联想到它的危害。
3. Measures of Central Tendency | 集中趋势度量
Mean: the arithmetic average, found by summing all data values and dividing by the number of values. It is commonly denoted by x̄ (x-bar) for a sample and μ (mu) for a population. The mean is sensitive to outliers. To remember: "Mean" is what you "mean" by average, but it can be pulled by extreme values.
平均数（均值）：把所有数据值相加再除以数据个数得到的算术平均值。样本平均数通常记为 x̄，总体平均数记作 μ。平均数对异常值敏感。记忆技巧：“Mean”就是日常说的平均，但一个极值就能把它拽跑。
Median: , it is the average of the two middle values. The median is robust against outliers. Think "Median = Middle" — like the central strip on a motorway.
中位数：将数据排序后位于中间位置的值。若数据个数n为奇数，则中位数为第 (n+1)/2 个值；若n为偶数，则为中间两个数的平均数。中位数不受极端值影响。记住“中位数”就是“正中间”的数。
Mode: the most frequently occurring value in the data. For grouped data, the modal class is the class interval with the highest frequency. "Mode" sounds like "most" — it is the value that appears most often. A data set can have one mode (unimodal), two modes (bimodal), or more.
众数：数据中出现次数最多的值。对于分组数据，众数类是频率最高的那个组距。众数的“众”就是“多”的意思，表示出现得最多。一组数据可以有一个众数（单峰）、两个（双峰）或更多。
4. Measures of Spread | 离散程度度量
Range: the simplest measure of spread, calculated as maximum value minus minimum value. It tells you the total width of the data but is heavily affected by outliers. Quick mental image: "range" is like the reach of an eagle’s wings — from tip to tip.
极差（全距）：最简单的离散度量，用最大值减去最小值。它告诉你数据的全幅，但极易受异常值影响。联想：“极差”就像鹰的两翼尖端之间的距离。
Interquartile range (IQR): ifference between the upper quartile (Q₃) and lower quartile (Q₁). It covers the middle 50% of the data, so it is a resistant measure of spread. IQR = Q₃ - Q₁. Use the memory cue: "IQR = Inner 50%" rtiles are found after arranging data in order; Q₁ is at position (n+1)/4, Q₃ at 3(n+1)/4.
四分位距（IQR）：上四分位数（Q₃）与下四分位数（Q₁）之差。它涵盖中间 50% 的数据，因而是抗干扰的离散度量。IQR = Q₃ - Q₁。记忆线索：“IQR 是 inner 50%”。先将数据排序，Q₁ 位于第 (n+1)/4 位置，Q₃ 位于 3(n+1)/4 位置。
Variance and Standard Deviation: he : variance is the average of squared deviations from the mean. For a sample, the formula is s² = Σ(xᵢ - x̄)² / (n - 1). The standard deviation is the square root of variance: s = √[Σ(xᵢ - x̄)² / (n - 1)]. It is the most commonly used measure of spread. The "n-1" (Bessel' an unbiased estimate. A small standard deviation means data points cluster near the mean.
方差与标准差：方差是各数据与均值之差的平方的平均值。样本方差公式为 s² = Σ(xᵢ - x̄)² / (n - 1)。标准差是方差的平方根：s = √[Σ(xᵢ - x̄)² / (n - 1)]。这是最常用的离散度量。样本方差分母用 n-1（贝塞尔校正）来得到无偏估计。标准差小意味着数据点聚集在均值附近。
5. Diagram and Chart Types | 图表类型
Bar chart: uses equal-width bars with gaps between them to represent frequencies of categorical or discrete data. The height of each bar shows the frequency. Remember: "Bar chart has a gap" — bars are separate. They are ideal for comparing categories that have no natural order.
条形图：用等宽且有间隙的条形表示分类或离散数据的频数，条形高度表示频数。记住：“条与条之间有缝隙”，适合比较无序分类。
Histogram: oportional to frequency, which means the vertical axis is frequency density (frequency ÷ class width) when class widths differ. A good trick: "Histogram = Height adjusted", referring to frequency density.
直方图：用于连续数据的区间分组图。与条形图不同，直方图的条形紧靠在一起体现连续性。每个条形的面积与频数成正比，因此当组距不等时，纵轴使用频率密度（频数 ÷ 组距）。记忆窍门：“直方图是面积表示频数，高度只是形式”。
Cumulative frequency diagram: a running total of frequencies plotted against the upper class boundaries. The curve allows you to estimate the median, quartiles, and percentiles. To recall its shape: it always goes up from left to right, never falling. Box-and-whisker plot (box plot): shows the five-number summary — minimum, Q₁, median, Q₃, maximum. Whiskers extend to the extremes within 1.5 × IQR, and any point beyond is an outlier.
累积频率图：将累积频数对组距上限描点而成。这条曲线可用于估算中位数、四分位数和百分位数。特点是从左到右只升不降。箱线图（盒须图）：展示五数综合——最小值、下四分位数、中位数、上四分位数、最大值。须线延伸至 1.5 倍 IQR 范围内最远的正常值，超出者标记为异常值。
6. Correlation and Regression | 相关与回归
Scatter diagram (scatter graph): a plot of paired (x, y) data used to examine the relationship between two variables. Each point represents one observation. Positive correlation means as x increases, y tends to increase; negative correlation means as x increases, y tends to decrease. No correlation appears as a random cloud.
散点图：将成对数据 (x, y) 绘在坐标轴上的图形，用于考察两个变量之间的关系。每个点代表一次观测。正相关表明 x 增大时 y 倾向增大；负相关表明 x 增大时 y 倾向减小；无相关则呈现无规律的散乱分布。
The correlation coefficient r to +1 (perfect positive). An r close to 0 suggests weak linear correlation. Quick memory: "r = relationship". However, correlation does not imply causation — just because two variables move together does not mean one causes the other.
相关系数 r 衡量线性关系的强度与方向。r 的取值范围在 -1（完全负相关）到 +1（完全正相关）之间。r 接近 0 表示线性相关性弱。记住 "r = 关系（relationship）"。但相关并不意味着因果——两个变量同向变化不等于一个导致另一个。
The line of best fit (regression line) is a straight line drawn through the scatter points to best represent the trend. It can be drawn by eye or calculated. Interpolation is using the line to estimate values within the data range, while extrapolation is predicting beyond that range. Extrapolation is less reliable. "Inter-" = inside, "Extra-" = outside.
最佳拟合线（回归线）是穿过散点表示总体趋势的直线，可以凭目测画出或计算得到。内插是在数据范围内使用该线估算值；外推是预测范围之外的值，外推可靠性较差。前缀 "Inter-" 表示内部，"Extra-" 表示外部，一目了然。
7. Probability and Chance | 概率与机会
Probability ÷ total number of possible outcomes, provided all outcomes are equally likely. A helpful trick: think of probability as "the fraction of luck".
概率衡量事件发生的可能性，范围从 0（不可能）到 1（必然）。在等可能结果的条件下，事件 A 的概率 P(A) = 有利结果数 ÷ 所有可能结果数。记忆：概率就是“运气的分数”。
Sample space is the set of all possible outcomes of an experiment. An event is a subset of the sample space. For rolling a die, the sample space is {1,2,3,4,5,6} and event "even number" is {2,4,6}. Mutually exclusive events cannot happen at the same time; if two events are mutually exclusive, P(A ∩ B) = 0. Think "cannot intersect". Independent events are those where the outcome of one does not affect the probability of the other, so P(A ∩ B) = P(A) × P(B).
样本空间是试验所有可能结果的集合。事件是样本空间的子集。掷一枚骰子，样本空间为 {1,2,3,4,5,6}，事件“偶数”为 {2,4,6}。互斥事件不能同时发生，若 A 和 B 互斥，则 P(A ∩ B) = 0，想想“无法相交”。独立事件指一个事件的发生不影响另一个事件的概率，此时 P(A ∩ B) = P(A) × P(B)。
Tree diagrams map out sequences of events and their probabilities. Probabilities multiply along branches, and you add probabilities for different paths to find total probability of a combined event. Remember "mushroom rule": multiply along, add between branches.
树状图用来描绘事件序列及其概率。沿分支概率相乘，不同路径的概率相加得到组合事件的总概率。记忆为“顺藤摸瓜”：沿分支相乘，跨分支相加。
8. Statistical Enquiry Cycle and Data Handling | 统计调查循环与数据处理
The statistical process often follows the PPDAC cycle: Problem (defining the question), Plan (designing data collection), Data (gathering and managing data), Analysis (calculating statistics, creating graphs), and Conclusion (interpreting findings, evaluating limitations). Many WJEC exam questions ask you to critique a given investigation using these stages.
统计过程通常遵循PPDAC 循环：问题（界定问题）、计划（设计数据收集方案）、数据（收集并整理数据）、分析（计算统计量、绘制图表）和结论（解读结果、评估局限性）。WJEC 考试常要求你用这些阶段去评论给定的调查过程。
Primary data is collected first-hand by the investigator for the specific purpose at hand (e.g., a survey you design). Secondary data by is data originally collected by someone else for a different purpose (e.g., government statistics, website data). Think "primary = personal", "secondary = shared".
初级数据（一手数据）是研究者为当前目的亲自收集的（如自己设计的问卷）。次级数据（二手数据）是别人出于其他目的收集的（如政府统计数据、网站资料）。记忆：初级是“自己的”，次级是“别人给的”。
Raw data are unprocessed measurements or observations straight after collection. Processed data have been organised, cleaned, or aggregated (e.g., frequencies, means). Outlier detection is a key step before drawing conclusions. An outlier ta point that lies an abnormal distance from the others, often identified as more than 1.5 × IQR below Q₁ or above Q₃.
原始数据是收集后未处理的测量或观察值。处理后的数据经过了整理、清洗或汇总（如频率、平均数）。在得出结论前，检测异常值是关键一步。异常值是远离其他数据点的值，通常用低于 Q₁-1.5×IQR 或高于 Q₃+1.5×IQR 来识别。
9. Describing Distributions | 描述分布
A symmetric distribution is mirror-like around its centre; the mean and median are roughly equal. The classic bell-shaped normal distribution is symmetric. A positively skewed (right-skewed) distribution has a long tail to the right, with mean > median > mode. A negatively skewed he left, with mean < median < mode. Mnemonic: the tail pulls the mean in its direction, so "positive skew = tail to the right, mean pulled right".
对称分布以中心为镜像，均值与中位数大致相等。典型的钟形正态分布是对称的。正偏态分布（右偏）的尾部向右延伸，均值 > 中位数 > 众数。负偏态分布（左偏）的尾部向左延伸，均值 < 中位数 < 众数。记忆口诀：“尾巴把均值拽过去”，所以正偏尾巴在右，均值就被拽到右边。
Bimodal distribution has two peaks, suggesting two subgroups in the data. A uniform distribution has roughly equal frequencies across all classes. The shape of a distribution helps you choose the best measure of central tendency; for skewed data, the median is more appropriate because the mean is distorted by extreme values.
双峰分布有两个峰，暗示数据包含两个子群体。均匀分布各类的频数大致相等。了解分布形状有助于选择最合适的集中趋势度量：偏态数据宜用中位数，因为均值会被极值扭曲。
Percentiles divide ordered data into 100 equal parts. The kth percentile is the value below which k% of the data fall. The 25th percentile is Q₁, the 50th percentile is the median, and the 75th percentile is Q₃. In cumulative frequency graphs, percentiles are estimated by reading across from the cumulative percentage point.
百分位数将排序后的数据分成 100 等份。第 k 百分位数是这样一个值，数据中有 k% 低于它。第 25 百分位即 Q₁，第 50 百分位即中位数，第 75 百分位即 Q₃。在累积频率图上，通过从累计百分比点水平划线可估计百分位数。
10. Graphs and Features for Comparison | 图形与比较特征
Time series graph: plots data points over time, often connected with lines to show trends. The x-axis always represents time. Trend refers to the long-term movement, while seasonal variation is a regular pattern that repeats at fixed intervals (e.g., monthly sales spikes). You might be asked to describe the trend ("increasing", "decreasing", "fluctuating").
时间序列图：描绘随时间变化的数据点，通常用线条连接以显示趋势。横轴始终表示时间。趋势指长期走向，而季节性变动是固定间隔内重复出现的规律（如每月销量激增）。考题常要求描述趋势（“上升”、“下降”、“波动”）。
Pie chart: es charts are useful for showing composition but poor for comparisons over time. Remember: "pie = parts of a whole".
饼图：将圆分割成扇形，扇形的角度代表该类别的比例。角度 = (频数 ÷ 总和) × 360°。饼图适合展示构成，但不适合跨时间比较。记住：“饼”就是整体的“块块”。
Comparative bar chart and multiple bar chart: used to compare frequencies across categories for two or more data sets. Bars are side-by-side for each category. Stacked bar chart places segments on top of each other within a bar to show total size and subgroup composition simultaneously. A simple visual clue: "stacked" means "piled up".
对比条形图和复合条形图：用于比较两个或多个数据集在不同类别上的频数。每个类别旁的条形并列放置。堆叠条形图则在同一个条形内叠加各段，以同时显示总量和子组构成。直观印象：“堆叠”就是“摞起来”。
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