📚 Year 8 OCR Statistics: Key Vocabulary Quick Guide | 八年级OCR统计：关键术语速记指南
Mastering the language of statistics is essential for success in Year 8 OCR mathematics. This quick guide covers the most important terms you will meet in data handling and probability. Each definition is paired with a Chinese translation to help bilingual learners memorise effectively.
掌握统计语言是八年级OCR数学成功的关键。本快速指南涵盖数据处理和概率中最重要的术语。每个定义都配有中文翻译，帮助双语学习者有效记忆。
1. Types of Average | 平均数的类型
An average is a single value that summarises a set of data. In Year 8 you will learn about three main averages: the mean, the median and the mode.
平均数是一个概括一组数据的单一数值。在八年级，你将学习三种主要的平均数：均值、中位数和众数。
Each average has its own strengths and is chosen depending on the type of data and what you want to find out.
每种平均数都有其优点，根据数据类型和你想了解的内容来选择。
2. Mean — The Balancing Point | 均值——平衡点
The mean is what most people call the ‘average’. It is calculated by adding up all the data values and then dividing by the number of values.
均值就是大多数人所说的”平均数”。它通过将所有数据值相加，然后除以数值的个数来计算。
Mean = sum of all data values ÷ number of data values
The mean behaves like a balancing point of the data set. If one value is much larger or smaller than the rest, the mean is pulled in that direction.
均值就像数据集的平衡点。如果有一个值比其他值大很多或小很多，均值就会被拉向那个方向。
In a symmetrical distribution, the mean, median and mode are often close together.
在对称分布中，均值、中位数和众数通常很接近。
3. Median — The Middle Value | 中位数——中间值
The median is the middle value when the data is arranged in order from smallest to largest.
中位数是将数据从小到大排列后位于中间的值。
If there are two middle numbers, the median is the mean of those two numbers.
如果有两个中间数，中位数就是这两个数的均值。
The median is not affected by extreme values (outliers), so it is often used for data like house prices or incomes.
中位数不受极端值（异常值）的影响，因此常用于房价或收入等数据。
4. Mode — Most Frequent | 众数——最频繁
The mode is the value that appears most often in a data set.
众数是数据集中出现次数最多的值。
A set of data can have one mode (unimodal), two modes (bimodal) or more than two modes (multimodal). If all values occur equally often, there is no mode.
一组数据可以有一个众数（单峰）、两个众数（双峰）或多于两个众数（多峰）。如果所有值的出现次数相同，则没有众数。
The mode is useful for non-numerical data, such as finding the most popular colour in a survey.
众数适用于非数值数据，例如在调查中找到最受欢迎的颜色。
5. Range — Spread of Data | 极差——数据分散程度
The range measures how spread out the data are. It is the difference between the largest and smallest values.
极差衡量数据的分散程度。它是最大值与最小值之间的差值。
Range = largest value − smallest value
A small range means the data are tightly clustered; a large range means they are widely spread.
极差小表示数据聚集紧密；极差大表示数据分布广泛。
Always subtract the smallest from the largest, and remember that range is a single number, not an interval.
始终用最大值减去最小值，并记住极差是一个数字，不是一个区间。
6. Frequency Tables | 频数表
A frequency table shows how often each data value occurs.
频数表显示每个数据值出现的次数。
Tally marks are often used to record frequencies before counting. Each group of five is shown as a diagonal line crossing four vertical lines, like this: |||| with a line through becomes a group of five.
在计数之前，通常使用 tally 标记来记录频数。每五个为一组，用一条斜线划过四条竖线表示，例如：|||| 加上一条斜线表示一组五。
Frequency tables make it easy to see which value is the mode and to calculate totals.
频数表让你很容易看出哪个值是众数，并方便计算总和。
7. Charts for Data: Bar Charts and Pie Charts | 数据图表：条形图和饼图
Bar charts display categorical data with rectangular bars where the height or length represents the frequency. The bars are separated by equal gaps to show that the categories are distinct.
条形图用矩形条显示分类数据，条的高度或长度表示频数。条形之间留出相等的间隙，以表明类别是独立的。
Pie charts show proportions of a whole. Each slice represents a category, and the angle of the slice is proportional to the frequency.
饼图显示整体的各个部分。每个扇形代表一个类别，扇形的角度与频数成比例。
To find the angle for a slice, use (category frequency ÷ total frequency) × 360°.
要计算扇形的角度，使用（类别频数 ÷ 总频数）× 360°。
8. Line Graphs and Scatter Graphs | 折线图与散点图
Line graphs are used to show how data changes over time. The horizontal axis usually shows time, and points are joined with straight lines.
折线图用于显示数据随时间的变化。横轴通常表示时间，各点用直线连接。
Scatter graphs (or scatter plots) show the relationship between two numerical variables. Each point on the graph represents a pair of values.
散点图（或散点图）显示两个数值变量之间的关系。图上的每个点代表一对值。
When interpreting a scatter graph, look for a pattern or trend. This can help you describe correlation.
解读散点图时，要寻找模式或趋势，这有助于你描述相关性。
9. Correlation — Seeing Relationships | 相关性——观察关系
Correlation describes the strength and direction of a relationship between two variables in a scatter graph.
相关性描述散点图中两个变量之间关系的强度和方向。
Positive correlation: as one variable increases, the other also tends to increase. The points slope upwards from left to right.
正相关：当一个变量增加时，另一个也倾向于增加。点从左到右向上倾斜。
Negative correlation: as one variable increases, the other tends to decrease. The points slope downwards.
负相关：当一个变量增加时，另一个倾向于减少。点从左到右向下倾斜。
No correlation: there is no clear pattern; the points are scattered randomly.
无相关：没有明显的模式；点随机分布。
Remember: correlation does not imply causation!
记住：相关关系不意味着因果关系！
10. Probability Basics: Experiment, Outcome, Event | 概率基础：试验、结果、事件
An experiment is a repeatable process that gives well-defined results, such as tossing a coin or rolling a dice.
试验是一个可重复的过程，产生明确定义的结果，例如抛硬币或掷骰子。
An outcome is a possible result of an experiment. Tossing a coin has two outcomes: heads or tails.
结果是试验的一个可能结果。抛硬币有两种结果：正面或反面。
An event is a set of one or more outcomes. Rolling an even number on a dice is an event containing the outcomes 2, 4, 6.
事件是一个或多个结果的集合。掷骰子得到偶数是包含结果2、4、6的事件。
Probability measures how likely an event is to happen. It is always a number between 0 (impossible) and 1 (certain).
概率衡量事件发生的可能性。它始终是介于0（不可能）和1（必然）之间的一个数字。
11. Sample Space and Randomness | 样本空间与随机性
The sample space is the set of all possible outcomes of an experiment. For a fair six-sided dice, the sample space is {1, 2, 3, 4, 5, 6}.
样本空间是试验所有可能结果的集合。对于一个公平的六面骰子，样本空间是{1, 2, 3, 4, 5, 6}。
When all outcomes are equally likely, the probability of an event is:
当所有结果可能性相同时，事件的概率计算公式为：
Probability = number of favourable outcomes ÷ total number of outcomes
‘Random’ means that every outcome has an equal chance of occurring, and the result cannot be predicted with certainty.
“随机”意味着每个结果发生的可能性均等，结果无法确切预测。
Using a sample space diagram (like a two-way table) helps list all outcomes for combined experiments, such as tossing two coins.
使用样本空间图（如双向表）可以帮助列出组合试验的所有结果，例如抛两枚硬币。
12. Quick Recap Table | 快速回顾表
| Term | English Definition | 中文释义 |
|---|---|---|
| Mean | Sum of values divided by number of values | 总和除以数值个数 |
| Median | Middle value when ordered | 排序后的中间值 |
| Mode | Most frequent value | 出现次数最多的值 |
| Range | Largest minus smallest value | 最大值减最小值 |
| Frequency | How often a value appears | 某个值出现的次数 |
| Bar chart | Graph with bars to show category frequencies | 用条形表示类别频数的图 |
| Pie chart | Circular chart showing proportions as slices | 用扇形显示比例的圆形图 |
| Scatter graph | Graph showing relationship between two variables | 显示两个变量关系的图 |
| Correlation | Describes strength and direction of a relationship | 描述关系的强度和方向 |
| Probability | Number from 0 to 1 measuring likelihood | 从0到1衡量可能性大小的数字 |
| Sample space | Set of all possible outcomes | 所有可能结果的集合 |
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