📚 Year 9 OCR Statistics: Key Vocabulary Rapid Review | Year 9 OCR 统计：词汇术语速记指南
Mastering the language of statistics is the first step to becoming confident with data. This guide covers the essential terms you will meet in the Year 9 OCR Statistics course, with clear definitions and helpful examples in both English and Chinese. Use it for quick revision or as a reference while tackling homework.
掌握统计学的语言是自信处理数据的第一步。本指南涵盖你在 Year 9 OCR 统计学课程中将遇到的核心术语，配有清晰的定义和示例，并提供中英双语对照。用于快速复习或作为完成作业时的参考资料。
1. Population and Sample | 总体与样本
A population is the entire set of individuals or items that we want to study. Because measuring everyone is often impossible, we select a sample – a smaller, manageable subset of the population. The sample must be representative for conclusions to be valid.
总体是我们想要研究的全部个体或项目的集合。由于通常不可能测量每一个人，我们会选取一个样本——即总体中一个较小、可操作的子集。为了使结论有效，样本必须具有代表性。
- Population: all students in your school. Sample: 50 students chosen at random.
- 总体：你所在学校的所有学生。样本：随机选出的 50 名学生。
2. Variable and Data Types | 变量与数据类型
A variable is any characteristic that can be measured or counted. Data can be categorical (qualitative) or numerical (quantitative). Numerical data is further split into discrete data, which can only take certain values (usually whole numbers), and continuous data, which can take any value within a range.
变量是指任何可以测量或计数的特征。数据可以分为类别（定性）数据或数值（定量）数据。数值数据进一步分为离散数据（只能取特定值，通常是整数）和连续数据（可以在一个范围内取任意值）。
- Categorical: eye colour, favourite subject.
- Discrete: number of books in a bag (0, 1, 2, …).
- Continuous: height of a plant (can be 12.3 cm, 12.35 cm).
- 类别数据：眼睛颜色、最喜欢的科目。
- 离散数据：书包里书的数量（0, 1, 2, …）。
- 连续数据：植物的高度（可以是 12.3 厘米、12.35 厘米）。
3. Frequency and Frequency Table | 频数与频数表
Frequency is the number of times a particular value or category occurs in a data set. A frequency table organises data by listing each item along with its frequency. Tally marks are often used when collecting data by hand.
频数是某个特定值或类别在数据集中出现的次数。频数表通过列出每个项目及其频数来整理数据。手工收集数据时，经常使用划记符号。
| Favourite Colour | Tally | Frequency |
|---|---|---|
| Blue | |||| | 4 |
| Red | || | 2 |
4. Mean, Median, Mode and Range | 平均数、中位数、众数和极差
These are the most common measures of central tendency and spread. The mean is the arithmetic average, calculated by summing all values and dividing by the number of values. The median is the middle value when data is ordered. The mode is the value that appears most often. The range is the difference between the largest and smallest values, showing how spread out the data is.
这些是最常见的集中趋势和离散程度的度量。平均数是通过将所有数值相加再除以数值的个数计算得出的算术平均值。中位数是数据排序后位于中间的值。众数是出现次数最多的值。极差是最大值与最小值之差，显示数据的分散程度。
Mean = (Sum of all values) ÷ (Number of values)
平均数 = (所有数值之和) ÷ (数值的个数)
Range = Largest value – Smallest value
极差 = 最大值 – 最小值
- Data: 3, 7, 7, 9, 14 → Mean = (3+7+7+9+14)/5 = 8; Median = 7; Mode = 7; Range = 14 – 3 = 11.
- 数据：3, 7, 7, 9, 14 → 平均数 = 8；中位数 = 7；众数 = 7；极差 = 11。
5. Probability Basics | 概率基础
Probability measures how likely an event is to happen, and is always a number between 0 and 1. A probability of 0 means impossible, 1 means certain. The probability of an event can be expressed as a fraction, decimal or percentage. The probability scale helps visualise this.
概率衡量一个事件发生的可能性大小，总是介于 0 和 1 之间的一个数字。概率为 0 表示不可能发生，1 表示必然发生。事件的概率可以用分数、小数或百分数表示。概率标尺有助于直观理解这一点。
P(Event) = Number of favourable outcomes ÷ Total number of possible outcomes
P(事件) = 有利结果的数量 ÷ 所有可能结果的总数
- Tossing a fair coin: P(Head) = ½ = 0.5 = 50%.
- 抛一枚公平硬币：P(正面) = ½ = 0.5 = 50%。
6. Experiment and Outcome | 试验与结果
In probability, an experiment is a repeatable process that gives rise to a set of results. Each possible result is called an outcome. The set of all possible outcomes is the sample space. An event is a collection of one or more outcomes, usually the ones we are interested in.
在概率中，试验是一个可重复进行的过程，会产生一系列结果。每一个可能的结果称为一个结果。所有可能结果的集合称为样本空间。事件是一个或多个结果的集合，通常是我们感兴趣的那些结果。
- Experiment: rolling a dice. Sample space: {1, 2, 3, 4, 5, 6}. Event “even number”: {2, 4, 6}.
- 试验：掷一个骰子。样本空间：{1, 2, 3, 4, 5, 6}。事件“偶数”：{2, 4, 6}。
7. Fair and Unfair | 公平与不公平
When all outcomes have the same probability of occurring, the event or device is described as fair. A fair coin or a fair dice is equally likely to show any face. If some outcomes are more likely than others, the process is biased or unfair. The term “equally likely” is a key phrase.
当所有结果发生的概率相同时，我们称这个事件或工具是公平的。一枚公平的硬币或一个公平的骰子，每一面出现的可能性相同。如果某些结果比其他结果更可能发生，那么这个过程就有偏差或不公平。“等可能性”是一个关键短语。
- A fair spinner with 4 equal sections gives each colour a probability of ¼.
- 一个有 4 个相等扇区的公平转盘，每个颜色出现的概率都是 ¼。
8. Charts and Graphs | 图表
Statistical diagrams help us visualise data. A bar chart uses bars to show frequencies of categorical or discrete data; the bars do not touch. A pictogram uses pictures to represent data. A pie chart shows proportions of a whole using sectors of a circle. A line graph plots points connected by lines, often used for time series. A scatter graph displays the relationship between two numerical variables.
统计图表帮助我们可视化数据。条形图用条形表示类别或离散数据的频数，条形之间不接触。象形图用图片表示数据。饼图用圆的扇形区域表示整体中各部分的比例。折线图将点用线连接起来，通常用于时间序列数据。散点图展示两个数值变量之间的关系。
- Bar chart: favourite pet of students. Pie chart: how a student spends their day.
- 条形图：学生最喜欢的宠物。饼图：一个学生一天的时间分配。
9. Scatter Graphs and Correlation | 散点图与相关性
A scatter graph shows paired values from two variables on the x- and y-axes. The pattern of points may reveal correlation. Positive correlation means as one variable increases, the other tends to increase. Negative correlation means as one increases, the other tends to decrease. No correlation means there is no clear pattern. Correlation does not imply causation.
散点图在 x 轴和 y 轴上显示两个变量的成对值。点的分布模式可能揭示相关性。正相关意味着当一个变量增加时，另一个也倾向于增加。负相关意味着当一个增加时，另一个倾向于减少。零相关意味着没有明显的模式。相关关系并不意味因果关系。
- Positive: height and shoe size (generally). Negative: speed and travel time.
- 正相关：身高和鞋码（一般情况）。负相关：速度和行驶时间。
10. Outlier | 异常值
An outlier is a data point that lies far away from the other values in the set. It may be due to measurement error or natural variation. Outliers can strongly affect the mean and range, so you need to decide carefully whether to include or exclude them in calculations.
异常值是数据集中远离其他数值的一个数据点。它可能是由于测量误差或自然变异引起的。异常值会极大地影响平均数和极差，因此你需要仔细决定在计算时是保留还是排除它们。
- Test scores: 70, 72, 74, 75, 76, 30. The score 30 is an outlier.
- 测试分数：70, 72, 74, 75, 76, 30。分数 30 是一个异常值。
11. Primary and Secondary Data | 一手数据与二手数据
Primary data is information you collect yourself for a specific purpose, such as through a survey or experiment. Secondary data is data that has already been collected by someone else, like census data or information from websites. Knowing the source helps assess reliability.
一手数据是你自己为特定目的而收集的信息，例如通过调查或实验获得。二手数据是别人已经收集好的数据，例如人口普查数据或来自网站的信息。了解来源有助于评估可靠性。
- Primary: measuring the handspan of classmates. Secondary: using published weather records.
- 一手数据：测量同学的手掌宽度。二手数据：使用已发布的天气记录。
12. Hypothesis and Conclusion | 假设与结论
In statistical investigations, we often start with a hypothesis – a prediction or statement that can be tested with data. After collecting and analysing data, we draw a conclusion about whether the evidence supports the hypothesis. A good conclusion refers back to the original question and acknowledges any limitations.
在统计调查中，我们通常先提出一个假设——一个可以用数据检验的预测或陈述。在收集和分析数据之后，我们会得出一个结论，说明证据是否支持该假设。一个好的结论会回扣最初的问题，并承认任何局限性。
- Hypothesis: “Year 9 boys spend more time on video games than Year 9 girls.” Collect data, compare means, then write conclusion.
- 假设：“九年级的男生比女生花更多时间玩电子游戏。” 收集数据，比较平均数，然后写出结论。
Published by TutorHao | Statistics Revision Series | aleveler.com
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