📚 Year 7 AQA Statistics: Quick-Reference Formula & Theorem Handbook | 七年级 AQA 统计：公式定理速查手册
This handbook brings together all the essential definitions, formulas and key ideas you will meet in the Year 7 AQA statistics course. Use it for quick revision, to check a formula before homework, or to build confidence when tackling data questions. Every section is written in clear English with a matching Chinese translation, so you can study in the way that suits you best.
这本手册汇集了七年级 AQA 统计课程中所有重要的定义、公式和关键概念。你可以用它进行快速复习、完成作业前核对公式，或在处理数据问题时建立信心。每一节都先用清晰的英语说明，再配上对应的中文翻译，方便你以最适合自己的方式学习。
1. Mean | 算术平均数
The mean is the average you get by sharing the total equally among all the data values. To find the mean, add up all the numbers and then divide by how many numbers there are.
算术平均数，就是把总数平均分配给每一个数据值得到的结果。求平均数时，先把所有数值加起来，再除以数值的个数。
Mean = (Sum of all values) ÷ (Number of values)
平均数 = 总和 ÷ 数据个数
If you have the numbers 4, 8, 6, the sum is 18 and there are 3 numbers, so the mean is 18 ÷ 3 = 6.
如果你有数字 4、8、6，总和是 18，共有 3 个数，那么平均数 = 18 ÷ 3 = 6。
2. Median | 中位数
The median is the middle value when the data values are arranged in order from smallest to largest. If there is an even number of values, the median is the mean of the two middle numbers.
把数据值从小到大依次排列后，处于中间位置的数值就是中位数。如果数据个数是偶数，中位数就是中间两个数的平均数。
For the list 3, 5, 7, the median is 5. For 2, 4, 6, 8, the two middle values are 4 and 6, so the median is (4 + 6) ÷ 2 = 5.
对于数列 3、5、7，中位数是 5。如果是 2、4、6、8，中间两个数是 4 和 6，所以中位数 = (4 + 6) ÷ 2 = 5。
3. Mode | 众数
The mode is the value that appears most often in a set of data. A set of data can have one mode, more than one mode (bimodal or multimodal), or no mode at all if no value repeats.
众数是一组数据中出现次数最多的数值。一组数据可能有一个众数、多个众数（双众数或多众数），也可能没有众数（如果没有数值重复出现）。
In the data 2, 3, 3, 5, 7, the mode is 3. In 1, 2, 3, 4 every number appears once, so there is no mode.
在数据 2、3、3、5、7 中，众数是 3。在 1、2、3、4 中，每个数只出现一次，因此没有众数。
4. Range | 极差（范围）
The range measures how spread out the data are. It is the difference between the largest value and the smallest value.
极差用来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
极差 = 最大值 − 最小值
If the highest score is 18 and the lowest is 5, the range is 18 − 5 = 13. A small range tells you the data are close together; a large range shows they are more spread out.
如果最高分是 18，最低分是 5，那么极差 = 18 − 5 = 13。极差小说明数据比较集中，极差大说明数据比较分散。
5. Probability – Basic Rule | 概率基本规则
Probability is a measure of how likely an event is to happen. It always lies between 0 and 1, where 0 means impossible and 1 means certain.
概率是衡量某个事件发生可能性的量，总是在 0 到 1 之间。0 表示不可能，1 表示一定发生。
Probability = Number of favourable outcomes ÷ Total number of possible outcomes
概率 = 有利结果的数量 ÷ 所有可能结果的总数
When you roll a fair six-sided die, the probability of rolling a 3 is 1/6, because there is one favourable outcome (rolling a 3) out of six possible outcomes.
掷一个均匀的六面骰子时，掷出 3 的概率是 1/6，因为有 1 种有利结果（掷出 3），总共有 6 种可能结果。
6. Frequency Table | 频数表
A frequency table organises data by showing how many times each value or category occurs. It often has three columns: value (or category), tally, and frequency.
频数表通过列出每个数值或类别出现的次数来整理数据。它通常包含三列：数值（或类别）、计数符号和频数。
Example: in a survey of favourite colours, red appears 5 times, blue 8 times, green 3 times. The frequency column simply records 5, 8 and 3. You can use tallies to help you count.
例如：在一项关于最喜欢颜色的调查中，红色出现 5 次，蓝色 8 次，绿色 3 次。频数列只需记录 5、8 和 3。你可以用划记符号来帮助计数。
7. Bar Chart | 条形图
A bar chart represents data with rectangular bars. The height (or length) of each bar shows the frequency or value of that category. Bars are usually separated by small gaps to show that the categories are distinct.
条形图用矩形条表示数据。每个条的高度（或长度）表示该类别的频数或数值。条与条之间通常留有小的间隔，以表明类别是互相独立的。
Remember: label both axes clearly, give the chart a title, and make sure the bar heights match the frequencies. Bar charts are ideal for comparing different categories such as favourite sports or types of pet.
记住：两条轴都要清楚地标上文字，为图表加上标题，并确保条的高度与频数一致。条形图非常适合比较不同类别，例如最喜欢的运动或宠物的种类。
8. Pie Chart | 饼图
A pie chart displays data as slices of a circle. The size of each slice (the angle at the centre) is proportional to the frequency of that category. The whole circle represents the total data set.
饼图以圆形切块的方式展示数据。每一块的大小（圆心角）与该类别的频数成比例。整个圆表示全部数据。
To calculate the angle for a slice: Angle = (Frequency of category ÷ Total frequency) × 360°
计算扇区的圆心角：圆心角 = (该类别的频数 ÷ 总频数) × 360°
If 10 out of 40 students like cats, the angle for cats is (10 ÷ 40) × 360° = 90°. Always check that the slices add up to 360°.
如果 40 名学生中有 10 人喜欢猫，那么猫对应的圆心角 = (10 ÷ 40) × 360° = 90°。一定要检查所有扇区的角度总和是否为 360°。
9. Line Graph | 折线图
A line graph is used to show how data change over time. Points are plotted and joined with straight lines. It is especially useful for spotting trends, such as rising or falling temperatures.
折线图用来展示数据随时间变化的情况。先描出数据点，再用直线依次连接起来。它对发现趋势尤其有用，比如温度升高或降低的变化。
Make sure the time intervals on the horizontal axis are equal. The vertical axis usually shows the quantity being measured. Look for peaks, dips and steady sections.
确保横轴上的时间间隔是相等的。纵轴通常表示被测量的量。注意观察图中的最高点、最低点以及平稳的部分。
10. Collecting Primary Data | 收集一手数据
Primary data is information you collect yourself for a specific purpose, such as conducting a survey, taking measurements or carrying out an experiment. It is original and has not been used before.
一手数据是你自己为了特定目的而收集的信息，比如开展调查、进行测量或做实验。它是原始的、之前未被使用过的数据。
Design clear questions, avoid leading questions that suggest an answer, and think about how you will record responses. A well-designed data collection sheet saves time and reduces mistakes.
设计清晰的问题，避免带有暗示性的问题，并考虑好如何记录回答。一张设计合理的数据收集表能节省时间并减少错误。
11. Discrete and Continuous Data | 离散数据与连续数据
Discrete data can only take certain separate values, usually whole numbers. Examples include the number of students in a class or the roll of a die. Continuous data can take any value within a range, such as height, mass or temperature.
离散数据只能取某些单独分开的值，通常是整数。例如班里学生的人数或掷骰子的点数。连续数据可以在一个范围内取任意值，如身高、质量或温度。
Why does it matter? Discrete data often suits bar charts or frequency tables, while continuous data can be grouped into intervals and shown on a histogram or line graph.
为什么这很重要？离散数据通常适合用条形图或频数表表示，而连续数据可以分组划入不同的区间，再用直方图或折线图呈现。
12. Choosing the Right Average | 选择恰当的平均数
Sometimes the mean, median or mode can give a better picture of the data. Choose the mean when you want a fair share; choose the median when there are outliers that might skew the mean; choose the mode to find the most popular choice.
有时候，平均数、中位数或众数能更好地反映数据特征。如果你想要公平分配，就选平均数；如果存在异常值可能拉偏平均数，就选中位数；如果要找出最受欢迎的选择，就选众数。
The mode is the only average you can use for non-numerical data, like colours or names.
对于颜色、名字这类非数值型数据，众数是唯一可以使用的平均数。
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