📚 Year 10 Cambridge Statistics: Vocabulary & Terminology Quick Guide | Year 10 剑桥统计：词汇术语速记指南
Mastering statistics starts with a solid grip on the language. This guide covers the essential vocabulary you will encounter in Year 10 Cambridge Statistics, from types of data to probability, giving you clear definitions and paired explanations in English and Chinese to speed up your revision and boost your exam confidence.
掌握统计学的第一步是牢固掌握其语言。本指南涵盖 Year 10 剑桥统计课程中会遇到的核心词汇，从数据类型到概率，提供中英对照的清晰定义和配对解释，帮助你快速复习并提升应试信心。
1. Types of Data | 数据类型
Data can be classified in several ways. Understanding the difference between qualitative and quantitative, discrete and continuous, and primary and secondary data is the foundation for choosing the right statistical methods.
数据有多种分类方式。理解定性数据与定量数据、离散数据与连续数据以及一手数据与二手数据的区别，是选择正确统计方法的基础。
Qualitative data describes qualities or categories and is non-numerical, such as eye colour or type of car.
定性数据描述性质或类别，是非数值型的，例如眼睛颜色或汽车类型。
Quantitative data is numerical and can be measured or counted. It is subdivided into discrete data, which can only take certain values (e.g. number of students), and continuous data, which can take any value within a range (e.g. height, time).
定量数据是数值型的，可以被测量或计数。它细分为离散数据（只能取特定值，如学生人数）和连续数据（可取范围内任意值，如身高、时间）。
Primary data is collected first-hand by the researcher for a specific purpose, while secondary data has been collected by someone else for a different purpose but is reused.
一手数据由研究者为特定目的直接收集，而二手数据则是由他人为其他目的收集后被再利用的。
2. Population and Sample | 总体与样本
In statistics, we rarely study every individual in a group. Key terms define the group we are interested in and the part we actually examine.
在统计学中，我们很少会研究一个群体中的每一个个体。关键术语定义了我们感兴趣的群体以及我们实际考察的部分。
A population is the entire set of individuals or items that we want information about. A sample is a smaller subset selected from the population. When every member of the population is surveyed, it is called a census.
总体是我们想获取信息的全部个体或项目的集合。样本是从总体中选出的一个较小子集。当调查总体中的每个成员时，就称为普查。
The sample must be representative of the population to avoid bias. Sampling frame is a list of all population members from which a sample can be drawn.
样本必须对总体具有代表性以避免偏差。抽样框是列出所有总体成员的清单，从中可以抽取样本。
3. Measures of Central Tendency | 集中趋势的度量
Averages summarise a dataset with a single typical value. The three main averages are the mean, median and mode, each with its own strengths.
平均数用单一典型值概括一个数据集。三种主要的平均数是均值、中位数和众数，各有优点。
The mean is the sum of all values divided by the number of values. It is calculated using the formula:
均值是所有数值之和除以数值个数。其计算公式为：
Mean = Σx ÷ n
The median is the middle value when the data are arranged in order. If there is an even number of values, it is the mean of the two middle numbers.
中位数是将数据按大小排列后位于中间的值。如果数据个数为偶数，则取中间两个数值的均值。
The mode is the value that appears most frequently. A set of data can have no mode, one mode (unimodal), or more than one mode (bimodal or multimodal).
众数是出现频率最高的值。一组数据可以没有众数，有一个众数（单峰），或有多个众数（双峰或多峰）。
4. Measures of Dispersion | 离散程度的度量
Knowing the spread of data is just as important as knowing the average. Dispersion tells us how varied the data are.
了解数据的分散程度与了解平均数同样重要。离散程度告诉我们数据的变异情况。
The range is the simplest measure: it is the difference between the largest and smallest values. It is sensitive to outliers.
极差是最简单的度量：它是最大值与最小值之差，但对异常值敏感。
The interquartile range (IQR) is the difference between the upper quartile (Q₃) and the lower quartile (Q₁). It measures the spread of the middle 50% of the data and is not affected by extreme values.
四分位距 (IQR) 是上四分位数 (Q₃) 与下四分位数 (Q₁) 之差，衡量中间 50% 数据的分散程度，且不受极端值影响。
Variance and standard deviation measure how much the data deviate from the mean. The standard deviation is the square root of the variance. Sample variance often uses the formula:
方差和标准差衡量数据偏离均值的程度。标准差是方差的平方根。样本方差常用公式：
s² = Σ(x – x̄)² ÷ (n – 1)
5. Frequency Distributions | 频率分布
Organising raw data into frequency tables and grouped frequency distributions is the first step in analysis. Here are the related terms.
将原始数据整理成频数表和组距式频率分布是分析的第一步。以下是相关术语。
Frequency is the number of times a value or category occurs. Relative frequency is the frequency divided by the total number of observations. Cumulative frequency is the running total of frequencies up to a certain point.
频数是某个数值或类别出现的次数。相对频率是用频数除以观测总数。累积频率是到某一点为止的频数累计和。
When data are grouped, we use class intervals or classes, such as 0-10, 10-20, etc. The class boundaries are the exact limits after considering gaps, and the class width is the difference between upper and lower boundaries. The midpoint of a class is used for estimating the mean from grouped data.
当数据分组时，我们使用组区间或组，如 0-10, 10-20 等。组界是考虑间隙后的精确界限，组距是上下组界之差。组的中点值用于从分组数据估算均值。
6. Charts and Graphs | 图表与图形
Different data types and purposes call for different visual representations. Misusing a chart can mislead; choosing correctly reveals patterns.
不同的数据类型和分析目的需要不同的可视化呈现方式。误用图表会误导；正确选择则能揭示模式。
A bar chart is used for categorical or discrete data, with gaps between bars. A histogram is for continuous data; bars touch and area represents frequency, so frequency density is used when class widths are unequal.
条形图用于分类数据或离散数据，条形之间有间隙。直方图用于连续数据；条形相连，面积代表频数，因此当组距不等时使用频率密度。
A pie chart shows proportions of a whole. A line graph shows trends over time. A scatter diagram displays the relationship between two numerical variables.
饼图展示整体中各部分的比例。折线图显示随时间变化的趋势。散点图呈现两个数值变量之间的关系。
A stem-and-leaf diagram preserves original data while showing the shape of the distribution. A box-and-whisker plot (box plot) displays the five-number summary: minimum, Q₁, median, Q₃, maximum.
茎叶图在保留原始数据的同时展示分布形态。箱线图（盒须图）呈现五数概括：最小值、Q₁、中位数、Q₃、最大值。
7. Cumulative Frequency and Percentiles | 累积频率与百分位数
Cumulative frequency analysis helps us find medians, quartiles and percentiles, which are vital for comparing data sets.
累积频率分析帮助我们找到中位数、四分位数和百分位数，这对于比较数据集至关重要。
A cumulative frequency table lists the running total of frequencies. A cumulative frequency curve (ogive) is a smooth curve plotted using upper class boundaries and cumulative frequency. The median is found at the 50th percentile, the lower quartile at the 25th percentile, and the upper quartile at the 75th percentile.
累积频率表列出了频数的累计值。累积频率曲线 (ogive) 是以组上界为横坐标、累积频率为纵坐标绘制的光滑曲线。中位数在 50ᵗʰ 百分位处找到，下四分位数在 25ᵗʰ 百分位处，上四分位数在 75ᵗʰ 百分位处。
A percentile is a value below which a given percentage of observations fall. The p-th percentile divides the data so that p% of the values lie below it.
百分位数是一个数值，低于该数值的观测值占给定的百分比。第 p 百分位数将数据分隔开，使得有 p% 的数据值在其下方。
8. Correlation and Line of Best Fit | 相关性与最佳拟合线
When examining relationships between two variables, correlation describes the strength and direction of the linear relationship.
在考察两个变量间的关系时，相关性描述线性关系的强度和方向。
Positive correlation means that as one variable increases, the other tends to increase. Negative correlation means that as one variable increases, the other tends to decrease. No correlation indicates no clear pattern.
正相关意味着一个变量增大时，另一个变量也趋于增大。负相关意味着一个变量增大时，另一个变量趋于减小。无相关表示没有明显模式。
The line of best fit on a scatter diagram is a straight line drawn to pass as close as possible to most points. It should have roughly equal numbers of points above and below the line. The line can be used for making predictions, but extrapolation beyond the data range is unreliable.
散点图上的最佳拟合线是一条尽可能靠近大多数点的直线，线上方和线下方的点数应大致相等。这条线可用于预测，但在数据范围之外进行外推是不可靠的。
The correlation coefficient (e.g. Pearson’s r) measures the strength of linear correlation on a scale from -1 to +1, though Year 10 often focuses on interpreting scatter diagrams by eye.
相关系数（如 Pearson r）在 -1 到 +1 的尺度上衡量线性相关的强度，不过 Year 10 通常侧重于通过目测解读散点图。
9. Basic Probability Terminology | 基础概率术语
Probability underpins statistical inference. Knowing the core vocabulary will help you solve problems involving chance and uncertainty.
概率是统计推断的支柱。掌握核心词汇将帮助你解决涉及机会和不确定性的问题。
An experiment is a repeatable process that gives rise to outcomes. An outcome is a possible result. The sample space is the set of all possible outcomes. An event is a subset of the sample space, often described by one or more outcomes.
试验是一个可重复的过程，会产生各种结果。结果是一种可能的情况。样本空间是所有可能结果的集合。事件是样本空间的一个子集，通常由一个或多个结果描述。
The probability of an event A is denoted P(A) and is calculated as:
事件 A 的概率记为 P(A)，计算公式为：
P(A) = Number of favourable outcomes ÷ Total number of outcomes
Mutually exclusive events cannot occur at the same time. Independent events have no influence on each other’s probabilities. The complement of A, written A’, is the event that A does not happen, with P(A’) = 1 – P(A).
互斥事件不能同时发生。独立事件相互不影响对方的概率。A 的对立事件，记为 A’，是 A 不发生的事件，且 P(A’) = 1 – P(A)。
10. Sampling Methods and Bias | 抽样方法与偏差
When collecting data from a sample, the method of selection greatly affects the reliability of conclusions. Bias must be minimised.
当从样本中收集数据时，选择方法极大影响结论的可靠性。必须尽量减少偏差。
Random sampling gives every member of the population an equal chance of being selected. Stratified sampling divides the population into groups (strata) and selects randomly from each in proportion to its size, ensuring representation of subgroups.
随机抽样让总体中每个成员有相等的被选中机会。分层抽样将总体分成若干组（层），并按比例从每一层中随机抽取，确保子群体的代表性。
Systematic sampling selects members at regular intervals from a list. Convenience sampling uses people who are easy to reach, which often introduces bias. Quota sampling requires interviewers to select a fixed number of people from specified categories but not randomly, which can also lead to bias.
等距抽样从名单中按固定间隔选取成员。便利抽样使用容易接触到的人，常常会引入偏差。配额抽样要求访调人员从指定类别中选取固定人数，但并非随机，同样可能导致偏差。
Bias is a systematic error that distorts results. Common types include selection bias (sample not representative), non-response bias (certain people do not reply), and measurement bias (faulty instrument or leading questions).
偏差是一种系统性误差，会扭曲结果。常见类型包括选择偏差（样本不具代表性）、无回答偏差（某些人不回复）和测量偏差（仪器故障或诱导性问题）。
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