📚 Year 10 Cambridge Statistics: Vocabulary & Terminology Quick Memorisation Guide | Year 10 剑桥统计：词汇术语速记指南
Mastering statistics starts with a solid grasp of its language. This guide breaks down the essential terms you will encounter in Year 10 Cambridge Statistics, pairing clear English definitions with Chinese explanations and memory hooks to speed up your revision.
掌握统计学从牢固理解其语言开始。本指南分解了你在 Year 10 剑桥统计课程中会遇到的核心术语，提供清晰的英文定义与中文解释，并搭配记忆技巧，帮助你快速复习。
1. Population & Sample | 总体与样本
A population is the complete collection of individuals, items, or data points that we wish to investigate. A sample is a smaller, manageable subset drawn from that population.
总体是我们希望研究的全部个体、项目或数据点的完整集合。样本是从总体中抽取的、便于处理的一个较小子集。
We usually study a sample because examining an entire population is too time‑consuming or costly. The sample must be representative – it should reflect the characteristics of the population as closely as possible – otherwise the conclusions may be biased.
我们通常研究样本，因为调查整个总体太耗时或成本太高。样本必须具有代表性——要尽可能反映总体的特征——否则结论可能带有偏差。
Quick memory trick: think of a chef tasting a spoonful of soup (sample) to judge the whole pot (population).
速记窍门：想象厨师尝一勺汤（样本）来判断整锅汤（总体）。
2. Variable Types: Discrete, Continuous, Categorical | 变量类型：离散、连续与分类
A variable is any characteristic that can be measured or counted. Discrete variables take only specific, separate values – usually integers. Examples: number of students in a class, shoe size.
变量是任何可以测量或计数的特征。离散变量只能取特定的、分离的值——通常是整数。例如：班级人数、鞋码。
Continuous variables can assume any value within a given range. Examples: height, mass, time, temperature. They are measured, not counted.
连续变量可以在给定范围内取任意值。例如：身高、质量、时间、温度。它们是测量得到的，而不是数出来的。
Categorical (qualitative) variables describe qualities or labels. They can be nominal (no natural order, like eye colour) or ordinal (ordered categories, like satisfaction ratings: poor, good, excellent).
分类（定性）变量描述性质或标签。它们可以是名义的（无自然顺序，如眼睛颜色）或有序的（有顺序的类别，如满意度评级：差、好、优秀）。
Mnemonics: ‘Discrete = dots on a graph; continuous = a smooth line.’ ‘Categorical starts with cat – think of putting cats into colour groups.’
助记法：“离散 = 图上的点；连续 = 一条光滑的线。”“分类以‘cat’开头，想想把猫咪按颜色分组。”
3. Measures of Central Tendency: Mean, Median, Mode | 集中趋势的度量：平均数、中位数、众数
The mean (arithmetic average) is found by summing all values and dividing by the number of items. For the data set {3, 5, 9}, mean = (3+5+9)/3 = 5.67.
平均数（算术平均值）是将所有数值相加后除以数据个数得到的。对于数据集 {3, 5, 9}，平均数 = (3+5+9)/3 ≈ 5.67。
The median is the middle value when the data are arranged in order. If there is an even number of observations, the median is the average of the two central numbers. For {3, 5, 9}, median = 5.
中位数是将数据按顺序排列后位于中间的值。如果数据个数为偶数，中位数则是中间两个数的平均数。对于 {3, 5, 9}，中位数 = 5。
The mode is the value that occurs most often. A data set may have one mode (unimodal), more than one (bimodal or multimodal), or none at all.
众数是出现次数最多的值。一组数据可能有一个众数（单峰）、多个众数（双峰或多峰），或者没有众数。
Memory aid: ‘Mean is mean because it involves adding and dividing; median is the middleman; mode sounds like most.’
记忆辅助：“Mean 是平均数，因为要加加减减；Median 是中间人‘middleman’；Mode 听起来像 most（最多）。”
4. Measures of Spread: Range, Quartiles & Interquartile Range (IQR) | 离散程度的度量：极差、四分位数与四分位距
The range is the simplest measure of spread: maximum value – minimum value. It is sensitive to extreme outliers.
极差是最简单的离散程度度量：最大值 − 最小值。它对极端异常值很敏感。
Quartiles split an ordered data set into four equal parts. Q₁ (lower quartile) is the median of the lower half, Q₂ is the median of the whole set, and Q₃ (upper quartile) is the median of the upper half.
四分位数将有序数据集分成四等份。Q₁（下四分位数）是下半部分的中位数，Q₂ 是整个数据集的中位数，Q₃（上四分位数）是上半部分的中位数。
The interquartile range (IQR) = Q₃ − Q₁. It describes the middle 50% of the data and is resistant to outliers.
四分位距 (IQR) = Q₃ − Q₁。它描述了中间 50% 的数据，并且不受极端值影响。
Visual mnemonic: draw a number line and label Q₁, Q₂, Q₃. Think ‘Q stands for quarter.’
视觉记忆：画一条数轴，标出 Q₁、Q₂、Q₃。记住“Q 代表 quarter（四分之一）”。
5. Advanced Dispersion: Variance & Standard Deviation | 高级离散度：方差与标准差
Variance measures the average squared deviation of each data point from the mean. For a population, it is σ² = Σ( xᵢ − μ )² ÷ N. For a sample, we use n−1 as the divisor.
方差衡量每个数据点与平均数之差的平方的平均值。对于总体，σ² = Σ( xᵢ − μ )² ÷ N；对于样本，除数用 n−1。
Standard deviation is the square root of the variance. It is expressed in the same units as the original data, making it easier to interpret. A small standard deviation indicates data points are clustered near the mean.
标准差是方差的平方根。它与原始数据使用相同单位，因而更容易解释。标准差小表示数据点集中在平均数附近。
Mnemonics: ‘Variance is squared – very volatile; standard deviation brings it back to earth.’ Remember: s for sample standard deviation, σ for population.
助记：“方差是平方差，因此非常不稳定；标准差把它拉回到现实中。”记住：s 表示样本标准差，σ 表示总体标准差。
6. Data Presentation: Frequency Tables, Bar Charts & Pie Charts | 数据展示：频数表、条形图与饼图
A frequency table lists categories or intervals alongside their counts (frequencies). Relative frequency is the proportion: frequency ÷ total number of observations.
频数表列出类别或区间及其计数（频数）。相对频数是比例：频数 ÷ 观察总数。
A bar chart uses rectangular bars of equal width to represent categorical data. The height of each bar corresponds to its frequency. Bars do not touch, emphasizing separate categories.
条形图用宽度相等的矩形条表示分类数据。每个条形的高度对应该类的频数。条形之间不接触，以强调它们是独立的类别。
A pie chart shows proportions as slices of a circle. Each slice angle = (category frequency ÷ total) × 360°. Pie charts work best when there are few categories.
饼图用圆形的扇形来显示比例。每个扇形的角度 = (类别频数 ÷ 总数) × 360°。饼图在类别较少时效果最好。
Memory hook: ‘Bar – separate like barrier; pie – portion of a circle you eat.’
记忆挂钩：“Bar（条形）像屏障一样分开；Pie（派）就像你可以吃掉的一块圆形。”
7. Histogram vs Bar Chart | 直方图与条形图的区别
A histogram is used for continuous or grouped discrete data. Unlike a bar chart, the bars touch, reflecting continuous intervals. The area of each bar is proportional to the frequency – on a frequency density histogram, the height equals frequency ÷ class width.
直方图用于连续数据或分组的离散数据。与条形图不同，直方图的条形紧挨在一起，反映连续的区间。每个条形的面积与频数成正比——在频率密度直方图中，高度 = 频数 ÷ 组距。
Key distinction: bar charts display categorical data with gaps between bars; histograms display numerical intervals with connected bars. If you see a space, it is a bar chart.
关键区别：条形图展示分类数据，条形之间有间隙；直方图展示数值区间，条形相连。你如果看到空隙，那就是条形图。
Interactive memory tip: ‘Histogram = height is not always frequency; you might need frequency density.’ For year 10, you often work with equal class widths, which makes them look similar, but remember the connection rule.
互动记忆提示：“直方图中高度不总是频数；可能需要频率密度。”在 Year 10 阶段，经常处理等组距，图形看起来很相似，但要记住条形是否接触的规则。
8. Relationships Between Variables: Scatter Plots, Correlation & Regression | 变量间的关系：散点图、相关与回归
A scatter plot shows paired numerical data as points on a coordinate grid. It helps visualise whether there is a relationship (correlation) between two variables.
散点图将成对的数值数据用坐标点表示。它有助于直观地看出两个变量之间是否存在关系（相关性）。
Correlation describes the strength and direction of a linear relationship. Positive correlation: as one variable rises, the other tends to rise. Negative correlation: as one rises, the other tends to fall. No correlation means there is no clear pattern.
相关性描述线性关系的强度和方向。正相关：一个变量增加，另一个也倾向增加。负相关：一个变量增加，另一个倾向减少。无相关表示没有明显模式。
A line of best fit (regression line) can be drawn through the points to model the relationship and make predictions. The equation is often y = a + bx, where b is the gradient.
可以通过这些点画出最佳拟合线（回归线），用于建模和预测。方程通常为 y = a + bx，其中 b 是斜率。
Recall: ‘Scatter shows the dots; correlation is the pattern; regression draws the line. Remember: correlation is not causation.’
回忆要点：“散点图展示点；相关性展示模式；回归画出直线。记住：相关不代表因果关系。”
9. Probability Basics: Experiment, Outcome, Event | 概率基础：试验、结果、事件
An experiment (or trial) is any procedure that produces a set of results. Examples: tossing a coin, rolling a die.
试验（或尝试）是产生一组结果的任何过程。例如：抛硬币、掷骰子。
An outcome is a single possible result of an experiment. Rolling a die has six outcomes: 1, 2, 3, 4, 5, 6.
结果是试验的一个可能结果。掷一粒骰子有六种结果：1, 2, 3, 4, 5, 6。
An event is a set of one or more outcomes. For example, ‘rolling an even number’ = {2, 4, 6}. The probability of an event A is written P(A) and is always between 0 and 1 inclusive.
事件是一组一个或多个结果的集合。例如，“掷出偶数” = {2, 4, 6}。事件 A 的概率记作 P(A)，且永远在 0 到 1 之间（包括 0 和 1）。
Memory chain: ‘Experiment produces many outcomes; an event selects some of them.’ Use a probability scale from impossible (0) to certain (1).
记忆链：“试验产生许多结果；事件从中挑选一些。”使用概率尺度从不可能(0)到必然(1)。
10. Probability Rules: Independent & Mutually Exclusive Events | 概率规则：独立事件与互斥事件
Mutually exclusive events cannot happen at the same time. If A and B are mutually exclusive, P(A and B) = 0, and P(A or B) = P(A) + P(B). Example: rolling a 2 and an odd number on a single die are mutually exclusive.
互斥事件不能同时发生。若 A 和 B 互斥，则 P(A 且 B) = 0，且 P(A 或 B) = P(A) + P(B)。例如：在一粒骰子上掷出 2 和掷出奇数就是互斥事件。
Independent events are those where the occurrence of one does not affect the probability of the other. For independent A and B, P(A and B) = P(A) × P(B). Tossing a fair coin twice: the second toss is independent of the first.
独立事件指一个事件的发生不影响另一个事件发生的概率。若 A 与 B 独立，则 P(A 且 B) = P(A) × P(B)。抛一枚均匀硬币两次：第二次抛掷的结果与第一次独立。
Common pitfall: ‘Mutually exclusive’ does not mean ‘independent’. If two events are mutually exclusive and both have non‑zero probability, they cannot be independent (knowing one occurred tells you the other did not).
常见误区：“互斥”不等于“独立”。如果两个事件互斥且概率都非零，它们不可能是独立的（因为知道一个发生，就知道另一个没有发生）。
Memory aid: ‘Mutually exclusive = can’t share a table; independent = don’t influence each other’s decisions.’
记忆方法：“Mutually exclusive 就像不能共用一张桌子；independent 就像互不影响彼此的决定。”
Published by TutorHao | Statistics Revision Series | aleveler.com
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