📚 Year 9 Edexcel Statistics: Key Terms Quick-Memorisation Guide | 九年级 Edexcel 统计：核心词汇速记指南
Welcome to your ultimate quick-memorisation guide for Year 9 Edexcel Statistics. Building confidence starts with knowing exactly what each term means and how to use it. This guide breaks down the essential vocabulary into logical groups and reinforces every term with simple definitions and memory hooks. Keep it handy while revising, and you will soon find statistical language second nature.
欢迎阅读九年级 Edexcel 统计核心词汇速记指南。建立信心的第一步就是精准掌握每一个术语的含义和用法。本指南把必背词汇按逻辑分组，每个术语都配有简明定义和记忆窍门。复习时随时翻阅，统计语言很快就会变成你的第二天性。
1. Data Types & Variables | 数据类型与变量
Qualitative data describes qualities or categories without numbers, like eye colour (blue, brown) or types of pet. Think ‘quality’ not ‘quantity’. Memory tip: Qualitative = Quality.
定性数据描述的是品质或类别，不使用数值，比如眼睛颜色（蓝色、棕色）或宠物种类。记住：定性 = 品质。
Quantitative data is numerical and can be counted or measured. It splits further into discrete data (countable whole-number values, e.g. number of students) and continuous data (measured on a scale, e.g. height, time). Discrete has gaps between possible values, while continuous can take any value in a range.
定量数据是数值型的，可以计数或测量。它又分为离散数据（可数的整数值，如学生人数）和连续数据（在标尺上测量，如身高、时间）。离散数据的可能值之间有间隔，而连续数据在一个范围内可以取任意值。
The table below summarises the classification:
| Type | Description | Example |
|---|---|---|
| Qualitative (Categorical) | Non-numerical labels | Favourite subject |
| Quantitative Discrete | Countable whole numbers | Number of siblings |
| Quantitative Continuous | Measured on a scale | Distance travelled |
下表总结了分类：数据类型、描述及例子。
2. Collecting Data | 数据收集方法
Primary data is collected first-hand by the researcher for a specific purpose. For example, conducting a survey with your classmates. Memory tip: ‘Primary’ = ‘Pioneer’ – you are the first to gather it.
原始数据是研究者为特定目的亲自收集的第一手数据。例如，向同班同学做问卷调查。记忆：原始 = 最先收集。
Secondary data is obtained from existing sources, such as government websites or textbooks. It saves time but may not perfectly match your investigation needs. Think ‘Secondary’ = ‘Second-hand’.
二手数据来自已有的来源，如政府网站或教科书。它节约时间，但可能不完全符合你的调查需求。联想“二手” = 别人已经用过的。
A questionnaire is a common tool for collecting primary data. The questions must be clear and unbiased to obtain reliable responses.
问卷是收集原始数据的常用工具。问题必须清晰且不带偏见，才能获得可靠的回答。
3. Measures of Central Tendency | 集中趋势度量
The three Ms – Mean, Median, and Mode – describe the centre of a data set. The mean is the arithmetic average, calculated by adding all values and dividing by the number of values.
三个M——平均数、中位数和众数——用来描述数据集的中心。平均数即算术平均值，把所有数值相加再除以数值的个数。
Mean = Σx ÷ n
（总和除以项数）
The median is the middle value when the data is ordered from smallest to largest. If there is an even number of values, the median is the midpoint of the two middle values.
中位数是将数据从小到大排序后位于正中间的值。如果数据个数为偶数，则取中间两个数的中点。
The mode is the value that appears most frequently. A data set can have one mode (unimodal), more than one mode (bimodal or multimodal), or no mode at all if no value repeats.
众数是出现次数最多的值。一个数据集可以有一个众数、多个众数（双众数或多众数），也可以没有众数（无重复值）。
Memory aid: ‘Mona the Mediator’ – Mode is Most common, Median is Middle, Mean is the Measurement average.
记忆妙招：“众数最常见，中位在中间，平均算总和”——用谐音联想即可牢牢记住。
4. Measures of Spread | 离散程度度量
The range tells us how spread out the data is. It is the difference between the highest and lowest values.
极差反映数据的分散程度。它是最大值与最小值之差。
Range = max − min
（极差 = 最大值 − 最小值）
An outlier is a data point that lies an abnormal distance from the rest of the values. An outlier can pull the mean up or down significantly, making the median a more robust measure in such cases.
离群值是与其它数据点距离异常远的数值。离群值会大幅拉高或拉低平均数，因此这种情况下中位数更稳健。
Understanding spread alongside an average gives a much clearer picture of the data. A small range indicates consistency; a large range shows high variability.
同时关注集中趋势和离散程度，才能全面理解数据。极差小说明数据一致，极差大则变异性高。
5. Types of Averages and When to Use Them | 平均数的选择时机
Use the mode when you need the most popular category, such as the most sold t-shirt size. The mode works for qualitative and quantitative data.
当需要最流行的类别时使用众数，例如最畅销的T恤尺码。众数适用于定性和定量数据。
Use the median when the data contains extreme values or is skewed, for example house prices or salaries. The median is resistant to outliers.
当数据含有极端值或分布偏斜时使用中位数，比如房价或工资。中位数不怕离群值干扰。
Use the mean when the data is roughly symmetric and has no significant outliers. It uses all values, so it is especially useful for further statistical calculations.
当数据大致对称且无明显离群值时使用平均数。它用到了所有数值，因此特别适合进一步的统计计算。
Quick decision rule: outfit choice → mode; typical salary → median; calculating an average score → mean.
快速决策口诀：选最火款式用众数；看普遍工资用中位数；算平均分数用平均数。
6. Frequency Tables & Grouped Data | 频数表与分组数据
A frequency table lists data values alongside the number of times each value occurs. It makes patterns easier to spot than a raw list.
频数表列出数据值及其出现的次数，比起原始清单更容易发现规律。
When data covers a wide range, we use grouped frequency tables. Data is organised into class intervals such as 0 ≤ x < 10, 10 ≤ x < 20. The modal class is the interval with the highest frequency.
当数据跨度很大时，我们使用分组频数表，将数据归入组距，如 0 ≤ x < 10, 10 ≤ x < 20。众数组就是频数最高的组距。
With grouped data we cannot calculate the exact mean; we estimate it using the midpoint of each class.
对于分组数据无法计算精确平均数，而是用各组的组中值进行估算。
Estimated Mean = Σ(f × m) ÷ Σf
（f = 频数, m = 组中值）
Remember to use equal class widths when drawing histograms, otherwise the area representation could be misleading.
记住，绘制直方图时组距必须相等，否则面积表示频率时会扭曲真实分布。
7. Statistical Diagrams Part 1: Bar Charts & Pie Charts | 统计图第一部分：条形图与饼图
A bar chart represents categorical (qualitative) data with rectangular bars. The bars have equal width and there are gaps between them, signalling that the categories are distinct.
条形图用长方形条代表分类（定性）数据。条形宽度相等且条与条之间有间隔，表示类别彼此独立。
A pie chart displays data as slices of a circle, where each slice’s angle is proportional to the frequency. The entire circle (360°) represents the total.
饼图把数据表现为圆形的扇形，每个扇形的角度与频数成比例。整个圆（360°）代表总量。
Sector angle = (Frequency ÷ Total frequency) × 360°
（扇形角度 = (频数 ÷ 总频数) × 360°）
Bar charts are ideal for comparing sizes of different categories at a glance; pie charts excel at showing how a whole is divided into parts.
条形图适合一目了然地比较不同类别的大小；饼图擅长展示整体如何被分割成若干部分。
8. Statistical Diagrams Part 2: Histograms & Stem-and-Leaf | 统计图第二部分：直方图与茎叶图
A histogram looks like a bar chart but is used for continuous quantitative data. The bars touch to indicate that the data scale is continuous, and the area of each bar represents frequency.
直方图外形像条形图，但用于连续型定量数据。条形紧挨着，表示数据刻度是连续的，每块面积代表频数。
In Year 9 we often work with histograms that have equal class widths, so bar heights directly represent frequency. Later you will learn about frequency density when widths vary.
九年级阶段通常处理组距相等的直方图，条形高度直接代表频数。将来组距不等时才会引入频率密度的概念。
A stem-and-leaf diagram preserves the original data values while organising them in order. The ‘stem’ represents the leading digit(s) and the ‘leaf’ the final digit. A key explains the representation.
茎叶图既能保留原始数据值，又能将它们有序排列。“茎”表示前几位数字，“叶”表示最后一位数字。图中必须附上图例说明。
Stem-and-leaf plots quickly reveal the shape of a distribution and make it easy to find the median and mode without losing the initial data.
茎叶图能迅速展现数据分布形态，便于找到中位数和众数，且不会丢失初始数据。
9. Scatter Graphs & Correlation | 散点图与相关性
A scatter graph plots paired numerical data on an x-y plane. Each dot represents one pair of values, helping us see relationships between two variables.
散点图将成对数值绘制在直角平面上。每个点代表一组数值对，帮助我们观察两个变量之间的关系。
Correlation describes the direction and strength of the relationship. Positive correlation means as one variable increases, the other tends to increase. Negative correlation means as one variable rises, the other generally falls. No correlation implies no apparent pattern.
相关性描述关系的方向和强弱。正相关意味着一个变量增大时另一个也倾向于增大；负相关则是一个增大而另一个减小；无相关表示看不出明显的联系模式。
A line of best fit (trend line) is drawn through the points to summarise the relationship and make predictions. Using this line to estimate inside the data range is interpolation; predicting beyond the range is extrapolation, which is less reliable.
最佳拟合线（趋势线）穿过数据点，用于总结关系并做预测。在数据范围内进行估计叫内插法；超出范围预测叫外推法，其可靠性较低。
Scatter graphs do not join the dots like a line graph; they keep them separate to reveal correlation.
散点图不像折线图那样连接点，而是让点保持独立以显露相关程度。
10. Probability Language & Scale | 概率语言与尺度
Probability measures how likely an event is to happen. It is expressed as a number between 0 and 1, or as a fraction, decimal or percentage.
概率衡量事件发生的可能性。它用一个介于 0 和 1 之间的数字表示，也可以用分数、小数或百分数表达。
Probability = Number of successful outcomes ÷ Total number of possible outcomes
概率 = 成功结果数 ÷ 所有可能结果总数
Key terms: impossible (probability 0), unlikely (close to 0), even chance (½), likely (close to 1), and certain (probability 1). A probability scale can be drawn to visualise these categories.
关键术语：不可能（概率 0），不太可能（接近 0），等可能（½），很可能（接近 1），必然（概率 1）。我们可以画出概率标尺来直观展示这些分类。
Probabilities can be written as fractions like ½, decimals like 0.5, or percentages like 50%. Always simplify fractions where possible.
概率可写成分数如 ½、小数 0.5 或百分数 50%。分数记得要化简。
11. Sampling Methods & Bias | 抽样方法与偏差
A population is the entire set of individuals or items we want information about. A sample is a subset of that population, used to draw conclusions without surveying everyone.
总体是我们想了解的全部个体或物品的集合。样本是总体的一个子集，用于在不必调查所有人的情况下得出结论。
A random sample gives every member of the population an equal chance of being selected. It is the best way to avoid bias, where some members are systematically favoured or excluded.
随机样本让总体中每个成员都有同等机会被选中。这是避免偏差的最佳方式——偏差意味着某些成员被系统地偏袒或排除。
Bias can creep in through convenience sampling (choosing only easy-to-reach people) or voluntary response (people choose themselves). Always ask: does every member really have a fair chance?
偏差可能通过便利抽样（只选容易接触到的人）或自愿回应（人们自主参加）悄悄混入。始终要问：每个成员真的都有公平的机会吗？
A larger sample size generally provides a more accurate picture, but only if it is random and representative.
较大的样本容量通常能给出更准确的图景，但前提是样本必须随机且具代表性。
12. The Data Handling Cycle | 数据处理循环
Statistical investigations follow a logical cycle that helps us draw meaningful conclusions. Edexcel highlights a structured approach: Plan → Collect → Process → Discuss.
统计调查遵循一个逻辑循环，帮助我们得出有意义的结论。Edexcel 强调的方法是：计划 → 收集 → 处理 → 讨论。
In the planning stage, you state a hypothesis, decide what data to collect, and consider how to collect it fairly. At collection, you gather primary or secondary data using appropriate tools like questionnaires or observations.
在计划阶段，你提出假设，决定收集什么数据，并考虑如何公平地收集。在收集阶段，用问卷或观察等合适工具获取一手或二手数据。
Processing the data involves organising it into tables, drawing diagrams, and calculating statistics like the mean or range. Finally, discussing means interpreting your findings, relating them back to the original hypothesis, and acknowledging any limitations or possible bias.
处理数据包括将其整理成表格、绘制图表并计算平均数、极差等统计量。最后，讨论是指解读发现，把它们与最初假设关联起来，并承认任何局限或可能的偏差。
Remember the loop is not strictly linear – you may revisit earlier stages when new questions emerge. This cycle is the backbone of all statistical reasoning.
记住这个循环不是单向的——当新问题出现时，你可能需要回到前面的阶段。这个循环是所有统计推理的骨干框架。
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