📚 Year 8 CAIE Statistics: Vocabulary and Terminology Quick Reference Guide | 八年级 CAIE 统计：词汇术语速记指南
Mastering the language of statistics is the first step to solving data problems with confidence. In Year 8 CAIE Statistics, you will encounter terms that describe data, summaries, and chance. This quick reference guide presents each key term with a clear English definition and a paired Chinese explanation, helping you build a strong bilingual foundation for your exams.
掌握统计学的语言是自信解决数据问题的第一步。在八年级 CAIE 统计中，你会遇到描述数据、汇总和机会的术语。本速记指南为每个关键术语提供了清晰的英文定义和配对的中文解释，帮助你为考试打下坚实的双语基础。
1. Key Measures of Central Tendency and Spread | 集中趋势和离散程度的核心度量
When you have a set of numbers, you often want to find a single number that represents the ‘middle’ or ‘typical’ value, and you also want to know how spread out the values are.
当你有一组数字时，你通常想找到一个代表“中间”或“典型”值的数字，同时你也想知道这些数值的分散程度。
Mean – The mean is the average. Add all the values together and divide by the total number of values. For the data 2, 3, 6, 7, 12, the mean is (2+3+6+7+12) ÷ 5 = 30 ÷ 5 = 6.
平均数 – 平均数就是平均值。把所有数值加起来，再除以数值的总个数。对于数据 2, 3, 6, 7, 12，平均数为 (2+3+6+7+12) ÷ 5 = 30 ÷ 5 = 6。
Median – The median is the middle value when the data are arranged in order. For 2, 3, 6, 7, 12, the median is 6. If there is an even number of values, the median is the average of the two middle numbers.
中位数 – 中位数是将数据按顺序排列后位于中间的值。对于 2, 3, 6, 7, 12，中位数是 6。如果数据个数为偶数，则中位数为中间两个数的平均值。
Mode – The mode is the value that appears most often. In a set like 2, 3, 3, 6, 7, the mode is 3. A data set can have more than one mode or no mode at all.
众数 – 众数是出现次数最多的值。在 2, 3, 3, 6, 7 这组数据中，众数是 3。一组数据可以有多个众数，也可以没有众数。
Range – The range is a measure of spread. Subtract the smallest value from the largest value. For 2, 3, 6, 7, 12, the range is 12 – 2 = 10.
极差 – 极差是衡量数据分散程度的量。用最大值减去最小值。对于 2, 3, 6, 7, 12，极差为 12 – 2 = 10。
2. Types of Data | 数据类型
Before you can analyse data, you must recognise what type of data you are dealing with. This affects how you display and interpret it.
在分析数据之前，你必须先识别处理的数据类型。这会影响你展示和解释数据的方式。
Discrete data can only take certain separate values. You get it by counting. Examples: the number of cars in a car park, the number of goals scored in a match.
离散数据只能取特定的、不连续的数值。通过计数得到。例子：停车场里的汽车数量，一场比赛中的进球数。
Continuous data can take any value within a range and is obtained by measuring. Examples: height, mass, temperature, time.
连续数据可以在一个范围内取任意值，通过测量得到。例子：身高、质量、温度、时间。
Primary data is data you collect yourself for a specific purpose. It is often collected through questionnaires, interviews or experiments.
原始数据是你自己为特定目的而收集的数据。通常通过问卷、访谈或实验收集。
Secondary data is data someone else collected, which you use for your own investigation. Examples include information from the internet, newspapers or government reports.
二手数据是别人已经收集好的数据，你拿来用于自己的研究。例子包括来自互联网、报纸或政府报告的信息。
| Feature | Discrete Data 离散数据 | Continuous Data 连续数据 |
|---|---|---|
| How obtained 获取方式 | Counting 计数 | Measuring 测量 |
| Possible values 可能的值 | Specific separate numbers 特定的分离数值 | Any value in an interval 区间内任意值 |
| Examples 例子 | Shoe size, number of pets 鞋码、宠物数量 | Height, time taken to run 100m 身高、一百米跑用时 |
3. Data Collection Methods | 数据收集方法
Collecting data in a fair and organised way is essential for reliable conclusions. Here are the key terms you need to know.
以公平、有组织的方式收集数据对于得出可靠结论至关重要。以下是你需要了解的关键术语。
Survey – A method of gathering information by asking questions to a group of people. A survey might use a questionnaire or an interview.
调查 – 通过向一组人提问来收集信息的方法。调查可以使用问卷或访谈。
Questionnaire – A set of written questions designed to collect data. Questions should be clear and not lead the respondent to a particular answer.
问卷 – 一套为收集数据而设计的书面问题。问题应当清晰，不应引导回答者给出特定答案。
Population – The entire group of individuals or items you want to find out about. For example, all students in your school or all cars in a city.
总体 – 你想了解的全部个体或物品的集合。例如，你所在学校的所有学生，或一个城市的所有汽车。
Sample – A smaller group selected from the population to represent it. You collect data from the sample and use it to estimate what the whole population is like.
样本 – 从总体中选出的、代表总体的一个较小群体。你从样本中收集数据，并用它来估计整个总体的情况。
Census – A survey of every member of the population. It gives very accurate results but can be expensive and time-consuming.
普查 – 对总体中每个成员进行的调查。它给出非常精确的结果，但可能昂贵且耗时。
4. Organising Data: Tally Charts and Frequency Tables | 整理数据：计数表和频数表
Once you have collected raw data, you need to organise it so you can see patterns clearly. Tally charts and frequency tables are the first tools used.
收集到原始数据后，你需要将其组织起来，以便清晰地看到模式。计数表和频数表是最先使用的工具。
Tally chart – A chart that uses tally marks to record the frequency of each data value as you collect it. Every fifth mark is drawn diagonally across the previous four, making groups of five easy to count. For example, 3 is recorded as |||, and 5 is recorded as ||||/ .
计数表 – 用计数符号来记录收集过程中每个数据值出现频率的图表。每第五个标记斜划在前四个标记上，使每五一组易于清点。例如，3 记录为 |||，5 记录为 ||||/ 。
Frequency – The number of times a particular value or category occurs in a data set.
频数 – 某个特定值或类别在数据集中出现的次数。
Frequency table – A table that lists data values, the tally and the frequency for each value. It helps you summarise the data quickly.
频数表 – 列出数据值、计数符号和每个值的频数的表格。它帮助你快速汇总数据。
Grouped frequency table – When you have a lot of different values, you can group them into class intervals, such as 0–4, 5–9, etc. The table shows the frequency for each interval.
分组频数表 – 当有许多不同的值时，你可以将它们分入组距，如 0–4、5–9 等。表中显示每个组的频数。
Example frequency table: Score 1, Tally |||, Frequency 3; Score 2, Tally ||||/ , Frequency 5.
频数表示例：成绩1，计数 |||，频数3；成绩2，计数 ||||/ ，频数5。
5. Charts and Graphs: Pictogram and Bar Chart | 图表：象形图和条形图
Visual representations make data easier to compare and understand. Two common types are pictograms and bar charts.
可视化表现形式使数据更容易比较和理解。两种常见的类型是象形图和条形图。
Pictogram – A pictogram uses pictures or symbols to represent data. Each symbol stands for a certain number of items, and a key tells you what one symbol represents. If one circle represents 2 students, then 4 circles stand for 8 students.
象形图 – 象形图使用图画或符号来表示数据。每个符号代表一定数量的项目，图例会告诉你一个符号代表什么。如果一个圆代表 2 个学生，那么 4 个圆就代表 8 个学生。
Bar chart – A bar chart uses rectangular bars of equal width to show frequencies. The height of each bar corresponds to the frequency. The bars are separated by gaps, showing that the categories are distinct. Bar charts are used for discrete or categorical data.
条形图 – 条形图使用宽度相等的矩形条来表示频数。每个条的高度对应其频数。条与条之间有间隙，表明这些类别是彼此独立的。条形图用于离散数据或分类数据。
When drawing a bar chart, always label the axes and give the chart a title. The vertical axis usually shows the frequency.
绘制条形图时，务必标记坐标轴并为图表加标题。纵轴通常表示频数。
6. Charts and Graphs: Pie Chart and Line Graph | 图表：饼图和折线图
Other useful graphs for Year 8 include pie charts, which show proportions, and line graphs, which show changes over time.
八年级其他有用的图表包括表示所占比例的饼图，以及表示随时间变化的折线图。
Pie chart – A pie chart is a circle divided into sectors. Each sector represents a category, and its angle is proportional to the frequency of that category. To find the angle for a sector, use: angle = (frequency of category ÷ total frequency) × 360°.
饼图 – 饼图是一个被分成多个扇形的圆。每个扇形代表一个类别，其角度与该类别的频数成比例。计算扇形的角度使用：角度 = (该类别的频数 ÷ 总频数) × 360°。
Line graph – A line graph plots points that show data values at different times or for ordered categories and then connects the points with straight lines. It is particularly useful for showing trends, such as changes in temperature over a week.
折线图 – 折线图标出在不同时间或有序类别下数据值的点，然后用直线将这些点连接起来。它在显示趋势时特别有用，例如一周内气温的变化。
Always remember that line graphs are for continuous data or ordered categories, while bar charts are usually for distinct categories.
请始终记住，折线图适用于连续数据或有序类别，而条形图通常适用于独立的类别。
7. Scatter Graphs and Correlation | 散点图与相关关系
Scatter graphs help us look for a relationship between two sets of data. The pattern of the points tells us about correlation.
散点图帮助我们寻找两组数据之间的关系。点的分布模式能告诉我们相关关系。
Scatter graph – A scatter graph uses coordinates to plot two variables together. Each point on the graph represents one item, with one variable on the horizontal axis and the other on the vertical axis.
散点图 – 散点图用坐标系将两个变量一起标出。图上的每个点代表一个项目，一个变量在横轴上，另一个在纵轴上。
Correlation – The relationship between two variables shown by the pattern of points. 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. If the points are scattered randomly, there is no correlation.
相关关系 – 由点的分布模式显示的两个变量之间的关系。正相关意味着当一个变量增大时，另一个也倾向于增大。负相关意味着当一个变量增大时，另一个倾向于减小。如果点随机分布，则没有相关关系。
Line of best fit – A straight line drawn on a scatter graph that passes as close as possible to most of the points. It does not have to pass through all points but should show the general direction of the relationship.
最佳拟合线 – 在散点图上绘制的一条直线，尽可能靠近大多数点。它不必经过所有点，但应显示关系的总体方向。
8. Introduction to Probability | 概率入门
Probability is the study of chance. It gives us a way to measure how likely an event is to happen.
概率是研究机会的学科。它为我们提供了一种衡量事件发生可能性的方法。
Experiment – An experiment is a repeatable procedure that produces a set of possible results. Examples include rolling a dice, tossing a coin or spinning a spinner.
试验 – 试验是一个可重复的程序，它产生一组可能的结果。例子包括掷骰子、抛硬币或转动转盘。
Outcome – An outcome is a single possible result of an experiment. When you toss a coin, the possible outcomes are heads and tails.
结果 – 结果是试验的单个可能结果。抛一枚硬币时，可能的结果是正面和反面。
Sample space – The sample space is the set of all possible outcomes of an experiment. For rolling a fair six-sided dice, the sample space is {1, 2, 3, 4, 5, 6}.
样本空间 – 样本空间是一个试验所有可能结果的集合。对于掷一个公平的六面骰子，样本空间是 {1, 2, 3, 4, 5, 6}。
Event – An event is a specific outcome or a set of outcomes we are interested in. For instance, ‘rolling an even number’ on a dice is the event {2, 4, 6}.
事件 – 事件是我们感兴趣的特定结果或一组结果。例如，掷骰子时“掷出偶数”是事件 {2, 4, 6}。
Probability of an event – If all outcomes are equally likely, the probability (P) of an event is: P(event) = number of favourable outcomes ÷ total number of possible outcomes. The probability of rolling a 3 on a fair dice is ⅙.
事件的概率 – 如果所有结果都是等可能的，事件的概率 (P) 为：P(事件) = 有利结果的数量 ÷ 可能结果的总数。掷一个公平骰子得到 3 的概率是 ⅙。
9. Probability Scale: Impossible, Certain and Even Chance | 概率尺度：不可能
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