📚 Year 10 CAIE Statistics: Vocabulary & Terms Quick-Reference Guide | Year 10 CAIE 统计：词汇术语速记指南
Mastering the language of statistics is the first step to success in your Year 10 CAIE course. This guide breaks down the essential terms you will encounter in descriptive statistics and probability, with clear English definitions followed by Chinese translations to support bilingual learners. Use it to revise key vocabulary, improve your communication of statistical ideas, and build confidence for both coursework and examinations.
掌握统计学的语言是 Year 10 CAIE 课程成功的第一步。这份速记指南将你在描述性统计和概率中会遇到的核心术语一一拆解，每条术语先给出清晰的英文释义，再附上中文翻译，帮助双语学习者巩固理解。用它来复习重点词汇，提升你表达统计思想的能力，并为平时作业和考试树立信心。
1. Foundations of Statistics | 统计基础
Statistics is the discipline that concerns the collection, organisation, analysis, interpretation, and presentation of data. It turns raw numbers into meaningful information that supports decision-making.
统计学是研究数据的收集、整理、分析、解释和展示的学科。它将原始数字转化为有意义的信息，为决策提供依据。
Data (plural) are individual facts, statistics, or items of information, often numerical. The singular form is datum, though ‘data’ is commonly treated as both singular and plural in everyday usage.
数据（复数）是指单个的事实、统计数字或信息条目，通常是数值型的。单数形式为 datum，但在日常使用中 data 常被同时用作单数和复数。
A population is the complete set of individuals, objects, or measurements that are of interest in a study. A sample is a subset of the population, selected to represent the whole.
总体是研究中感兴趣的全部个体、对象或测量值的集合。样本是从总体中选出的一个子集，用以代表整体。
A census collects data from every member of the population, whereas a survey typically gathers information from a sample. A parameter is a numerical summary describing a population characteristic; a statistic describes a sample characteristic.
普查从总体中的每一个成员收集数据，而调查通常从样本中收集信息。参数是描述总体特征的数值概括；统计量是描述样本特征的数值概括。
2. Types of Data | 数据的类型
Categorical (qualitative) data represent characteristics or labels that can be divided into groups. Examples include eye colour, blood type, or favourite subject. Categorical data can be nominal (no natural order, like hair colour) or ordinal (natural order, like size: small, medium, large).
分类（定性）数据表示可以被划分为不同组别的特征或标签。例如眼睛颜色、血型或最喜欢的科目。分类数据可以是名义的（无自然顺序，如发色）或有序的（有自然顺序，如尺码：小、中、大）。
Numerical (quantitative) data consist of numbers that represent counts or measurements. Discrete data take only specific, separate values – usually whole numbers, like the number of students in a class. Continuous data can take any value within a given range, such as height, mass, or time.
数值（定量）数据由表示计数或测量的数字组成。离散数据只能取特定的、分隔的值——通常是整数，如班级学生人数。连续数据可以在给定范围内取任意值，例如身高、质量或时间。
Primary data are collected first-hand by the researcher for a specific purpose (e.g. conducting an experiment). Secondary data are data that have already been collected by someone else (e.g. government statistics, published research).
原始数据由研究者为一特定目的亲自收集（如进行实验）。二手数据是他人已经收集好的数据（例如政府统计数据、已发表的研究）。
3. Data Collection and Sampling | 数据收集与抽样
A simple random sample gives every member of the population an equal chance of being selected, often using random number generators or lottery methods. It reduces bias but can be impractical for large populations.
简单随机抽样使总体中的每个成员都有均等的机会被选中，通常使用随机数生成器或抽签方法。它能减少偏差，但对于大规模总体可能不切实际。
Stratified sampling divides the population into distinct subgroups (strata) that share a common characteristic, then takes a random sample from each subgroup proportional to its size. This ensures representation across key groups.
分层抽样将总体划分为具有共同特征的不同子群（层），然后按比例从每个子群中随机抽取样本。这确保了关键群体的代表性。
Systematic sampling selects individuals at regular intervals from an ordered list, for example every 10th name on a register. It is quick and simple, but may introduce patterns if the list has hidden periodicity.
系统抽样（等距抽样）从一个有序名单中按固定间隔选取个体，例如花名册上每第10个名字。它快速简便，但如果名单存在隐藏的周期性，可能引入模式偏差。
Convenience (opportunity) sampling uses individuals who are easiest to reach. It is cheap and fast, but often seriously unrepresentative. Voluntary response sampling invites people to participate, leading to self-selection bias.
便利（机会）抽样选取最容易接触到的个体。它成本低、速度快，但往往严重缺乏代表性。自愿回应抽样邀请人们自愿参加，容易导致自我选择偏差。
The sampling frame is the list of all members of the population from which the sample is drawn. Bias occurs when the sampling method systematically over- or under-represents certain groups, distorting results.
抽样框是总体所有成员的名单，样本即从中抽取。当抽样方法系统性地高估或低估某些群体时便会产生偏差，扭曲结果。
4. Organising Data | 数据整理
Frequency is the number of times a particular value or category appears in a data set. A frequency table lists all values and their frequencies, often with tally marks to aid counting.
频数是数据集中某个特定值或类别出现的次数。频数表列出所有值及其频数，通常伴有划记符以帮助计数。
Grouped data are organised into class intervals when there are many different values, especially for continuous data. The class width should be consistent, and intervals must not overlap.
当有许多不同取值时（尤其是连续数据），数据会被组织到组距中，形成分组数据。组距宽度应保持一致，区间不可重叠。
Relative frequency expresses frequency as a fraction, decimal, or percentage of the total. It helps compare distributions from samples of different sizes.
相对频数将频数表示为总数的一个分数、小数或百分数。它便于比较不同样本量下的分布。
Cumulative frequency is the running total of frequencies up to the end of each class interval. It is used to construct cumulative frequency curves (ogives) and to estimate medians, quartiles, and percentiles.
累积频数是到每个组距末尾为止的频数累计总和。它用于绘制累积频数曲线（折线图），并用于估算中位数、四分位数和百分位数。
5. Graphical Representations | 图表表示
A bar chart uses equal-width bars separated by gaps to represent categorical data. The height (or length) of each bar corresponds to its frequency or relative frequency. Gaps emphasise that categories are distinct, not continuous.
条形图使用等宽、有间隙的条形来表示分类数据。每个条形的高度（或长度）对应该类别的频数或相对频数。间隙强调了类别是分离的，而非连续的。
A histogram displays grouped continuous data (or discrete data with grouped intervals) using adjacent bars of equal class width; the area of each bar is proportional to frequency. Where class widths differ, frequency density must be plotted on the vertical axis (frequency ÷ class width).
直方图用相邻的等宽条形展示分组连续数据（或分组离散数据）；每个条形的面积与频数成正比。当组距宽度不同时，垂直轴必须绘制频率密度（频数 ÷ 组距）。
gle = (frequency / total) × 360°). Pie charts are best for showing proportions of a whole.
饼图是一个圆形图，每个类别由一个扇形表示；扇形角度与其频数成比例（角度 = (频数 / 总数) × 360°）。饼图最适合展示各部分在整体中所占的比例。
A line graph plots points joined by straight line segments, usually to show trends over time. Time is marked on the horizontal axis and the variable of interest on the vertical axis.
折线图用直线段连接各数据点，通常用于展示随时间变化的趋势。时间标在横轴上，所关注的变量标在纵轴上。
A scatter diagram (scatter plot) displays paired numerical data on coordinate axes to investigate the relationship between two variables. The pattern of points helps identify correlation.
散点图在坐标轴上展示成对的数值数据，以探究两个变量之间的关系。点的分布形态有助于识别相关性。
6. Measures of Central Tendency | 集中趋势的度量
The mean (arithmetic mean) is the sum of all values divided by the number of values. For a sample, it is often denoted by x̄ (x-bar). The mean uses every data point but is sensitive to extreme values (outliers).
平均值（算术平均数）是所有数值之和除以数值的个数。样本均值常用 x̄（x杠）表示。平均值使用了每个数据点，但对极端值（异常值）敏感。
The median is the middle value when the data are arranged in order. For an odd number of observations, it is the central value; for an even number, it is the average of the two middle values. The median is resistant to outliers, making it a better measure for skewed distributions.
中位数是将数据排序后位于中间的值。若数据个数为奇数，中位数就是正中间的值；若为偶数，则是中间两个值的平均数。中位数不受异常值影响，因此在偏态分布中是一个更好的度量。
The mode is the value that occurs most frequently in a data set. A set of data may have one mode (unimodal), two modes (bimodal), or more. The mode is the only measure of central tendency that can be used with nominal categorical data.
众数是数据集中出现最频繁的值。一组数据可以有一个众数（单峰）、两个众数（双峰）或更多。众数是唯一可用于名义分类数据的集中趋势度量。
7. Measures of Dispersion | 离散程度的度量
The range is the difference between the maximum and minimum values in a data set. It is the simplest measure of spread but is heavily influenced by outliers.
极差（全距）是数据集中最大值与最小值之差。它是最简单的离散度量，但极易受异常值影响。
Quartiles divide ordered data into four equal parts. The lower quartile (Q₁) is the median of the lower half of the data; the upper quartile (Q₃) is the median of the upper half. The second quartile (Q₂) is the median.
四分位数将有序数据分成四等份。下四分位数（Q₁）是数据下半部分的中位数；上四分位数（Q₃）是数据上半部分的中位数。第二个四分位数（Q₂）就是中位数。
The interquartile range (IQR = Q₃ – Q₁) measures the spread of the middle 50% sistant to extreme values and is often used alongside the median to summarise skewed data.
四分位距（IQR = Q₃ – Q₁）衡量中间50%数据的分散程度。它对极端值具有抵抗力，常与中位数一起用于总结偏态数据。
Variance measures the average squared deviation of each value from the mean. The formula for a population variance uses σ² (sigma squared); for a sample, s² is used. Standard deviation is the square root of the variance, returning the spread to the original units of measurement. A larger standard deviation indicates greater spread.
方差衡量各数值与平均值之间偏差平方的平均数。总体方差公式使用 σ²（西格玛平方）；样本方差使用 s²。标准差是方差的平方根，将离散程度还原为原始测量单位。标准差越大，表示数据越分散。
8. Skewness and Distribution Shape | 偏度与分布形态
A symmetrical distribution has its mean, median, and mode at the same central point, and the left and right sides of its histogram are mirror images. The normal distribution is a classic example.
对称分布的均值、中位数和众数重合于中心点，其直方图左右两侧互为镜像。正态分布是一个经典例子。
In a positively skewed (right-skewed) distribution, the longer tail extends to the right, and typically mean > median > mode. It often occurs when there is a lower boundary but no upper boundary, such as income data.
在正偏（右偏）分布中，长尾向右延伸，通常均值 > 中位数 > 众数。它常出现在有下限而无上限的情况下，如收入数据。
In a negatively skewed (left-skewed) distribution, the longer tail trails to the left, and typically mean < median < mode. An example might be the age at death from natural causes, where most people live to an old age and few die young.
在负偏（左偏）分布中，长尾向左拖曳，通常均值 < 中位数 < 众数。例如自然死亡年龄，多数人活到高龄，极少数早逝。
9. Introduction to Probability | 概率基础
Probability is a measure of the likelihood that an event will occur, expressed as a number between 0 (impossible) and 1 (certain). It can be written as a fraction, decimal, or percentage.
概率是衡量某一事件发生可能性的度量，用0（不可能）到1（必然）之间的数字表示。它可以写成分数、小数或百分数。
e complete set of all possible outcomes. For a fair six-sided die, S = {1, 2, 3, 4, 5, 6}.
试验是一个可重复的过程，能产生一组结果。样本空间（S）是所有可能结果的完整集合。对于一个公平的六面骰子，S = {1, 2, 3, 4, 5, 6}。
An event is a subset of the sample space – a collection of one or more outcomes that satisfy a particular condition. The complement of event A, written as A' or Aᶜ, is all outcomes not in A.
事件是样本空间的一个子集——满足特定条件的一个或多个结果的集合。事件A的补集，记作A' 或 Aᶜ，是所有不在A中的结果。
es). Experimental (relative frequency) probability is obtained by conducting trials: P(A) = (number of times A occurs) / (total number of trials). As the number of trials increases, experimental probability tends to approach theoretical probability (the law of large numbers).
理论概率通过对等可能结果的推理得出：P(A) = （有利结果数）/（总结果数）。试验（相对频数）概率通过进行试验获得：P(A) = （事件A发生的次数）/（试验总次数）。随着试验次数增加，试验概率会趋近于理论概率（大数定律）。
10. Correlation and Association | 相关与关联
Correlation describes the strength and direction of a linear relationship between two numerical variables. Positive correlation means that as one variable increases, the other also tends to increase. Negative correlation means that as one variable increases, the other tends to decrease.
相关描述了两个数值变量之间线性关系的强度和方向。正相关意味着一个变量增大时，另一个也倾向于增大。负相关意味着一个变量增大时，另一个倾向于减小。
Correlation does not imply causation. Just because two variables move together does not mean that one causes the other. A lurking variable may influence both, or the association may be coincidental.
相关不代表因果关系。两个变量同向变动并不意味着一个导致了另一个。可能存在一个潜变量同时影响两者，或者这种关联纯属巧合。
The correlation coefficient, r, is a numerical measure of linear correlation strength. It ranges from –1 (perfect negative linear correlation) through 0 (no linear correlation) to +1 (perfect positive linear correlation). For Year 10, you will mostly interpret scatter diagrams and recognise the approximate value of r from a given scale.
相关系数 r 是线性相关强度的数值度量。其取值范围从 –1（完全负线性相关）经 0（无线性相关）到 +1（完全正线性相关）。在 Year 10 阶段，你主要根据散点图判断相关情况，并依据给定标度识别 r 的近似值。
11. Misleading Statistics and Critical Thinking | 误导性统计与批判性思维
Graphs can be misleading if scales are truncated, axes do not start at zero, or pictograms use inconsistently sized area symbols. Always check the scale, labels, and source of data before drawing conclusions.
如果刻度被截断、坐标轴未从零开始或象形图使用了不一致的面积符号，图表就可能产生误导。在得出结论前，务必检查刻度、标签和数据来源。
Averages can be distorted by outliers or by choosing the 'wrong' average. For example, reporting the mean for house prices in an area with a few luxury estates can balloon the figure, hiding the typical price that the median would reveal.
平均值可能会被异常值或被选择“错误”的平均数所扭曲。例如，在一个有几处豪宅的地区报告房价均值会拉高数值，掩盖了中位数所反映的典型价格。
Sampling bias occurs when the sample is not representative of the population. Voluntary response, convenience samples, and under-coverage all lead to conclusions that cannot be generalised.
当样本不能代表总体时便出现抽样偏差。自愿回应、便利抽样和覆盖不全都会导致无法推广的结论。
12. Quick Review of Key Symbols and Notation | 关键符号与记号速览
Familiarity with notation saves time in exams. Here are some symbols you will meet frequently:
熟悉符号能在考试中节省时间。以下是你会经常碰到的符号：
| Symbol | Meaning | 中文含义 |
|---|---|---|
| x̄ | Sample mean | 样本均值 |
| μ | Population mean | 总体均值 |
| σ | Population standard deviation | 总体标准差 |
| s | Sample standard deviation | 样本标准差 |
| σ² | Population variance | 总体方差 |
| Σ | Summation (sum of values) | 求和（数值之和） |
| n | Sample size | 样本量 |
| N | Population size | 总体规模 |
| Q₁, Q₂, Q₃ | Lower, median, upper quartile | 下四分位数、中位数、上四分位数 |
| IQR | Interquartile range | 四分位距 |
| r | Correlation coefficient | 相关系数 |
These symbols form the language of statistics. As you progress, you will meet others such as p̂ (sample proportion) and s² (sample variance), but mastering the ones above will give you a strong foundation for CAIE Year 10 tasks.
这些符号构成了统计学的语言。随着学习的深入，你还会遇到 p̂（样本比例）和 s²（样本方差）等符号，但掌握以上这些将为你完成 CAIE Year 10 的练习打下坚实基础。
Published by TutorHao | Statistics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图