📚 Year 7 OCR Statistics: Quick Reference Handbook of Formulas and Theorems | Year 7 OCR 统计：公式定理速查手册
Welcome to your Year 7 OCR Statistics quick reference guide. This handbook brings together all the essential formulas, definitions and key ideas you need to master data handling. Keep it handy while you practise, and you will soon be confident working with averages, charts and data types.
欢迎使用你的七年级 OCR 统计速查手册。本手册汇集了你在数据处理中需要掌握的所有基本公式、定义和关键概念。练习时随身携带它，很快你就能自信地处理平均数、图表和数据类型。
1. Mean, Median, Mode and Range | 平均数、中位数、众数和极差
In Year 7 Statistics, you will encounter four key measures that summarise a set of data: the mean, median, mode and range. These help you understand the central tendency and spread of the data.
在七年级统计中，你会遇到概括一组数据的四个关键度量：平均数、中位数、众数和极差。它们帮助你了解数据的集中趋势和离散程度。
The mean is the arithmetic average, the median is the middle value, the mode is the most frequent value, and the range tells you how far apart the smallest and largest values are.
平均数是算数平均值，中位数是中间值，众数是最常出现的值，而极差则告诉你最小值和最大值之间有多远。
2. Calculating the Mean | 计算平均数
The mean is found by adding all the data values together and then dividing by the number of values. It is often called the average.
平均数是将所有数据值相加，然后除以数值的个数所得。它常被称为平均值。
Mean = sum of all values ÷ number of values
平均数 = 所有数值的总和 ÷ 数值的个数
For example, the mean of 3, 7, 8, 5 and 2 is (3+7+8+5+2) ÷ 5 = 25 ÷ 5 = 5.
例如，3、7、8、5 和 2 的平均数为 (3+7+8+5+2) ÷ 5 = 25 ÷ 5 = 5。
When you have a frequency table, multiply each value by its frequency, sum these products, then divide by the total frequency.
当你有一个频率表时，将每个值乘以其频数，把这些乘积相加，然后除以总频数。
3. Finding the Median | 求中位数
The median is the middle value when the data is arranged in order of size. If there is an even number of values, the median is the mean of the two middle numbers.
中位数是将数据按大小顺序排列后中间的那个值。如果有偶数个数值，中位数则是中间两个数的平均数。
For the data set 4, 9, 2, 7, 6, first order it: 2, 4, 6, 7, 9. The median is 6 (the third number).
对于数据集 4, 9, 2, 7, 6，先排序：2, 4, 6, 7, 9。中位数为 6（第三个数）。
If we add 11 to the set: 2, 4, 6, 7, 9, 11. The two middle values are 6 and 7, so median = (6 + 7) ÷ 2 = 6.5.
如果加入 11：2, 4, 6, 7, 9, 11。中间两个数是 6 和 7，所以中位数 = (6 + 7) ÷ 2 = 6.5。
Always sort the numbers first—this step is essential for finding the median correctly.
一定要先排序——这一步对正确求出中位数至关重要。
4. Identifying the Mode | 确定众数
The mode is the value that appears most frequently in a data set. There can be more than one mode, or no mode at all if all values occur only once.
众数是数据集中出现次数最多的值。可以有多个众数，或者如果所有值都只出现一次，则没有众数。
In the set 3, 5, 5, 7, 7, 7, 9, the mode is 7 because it appears three times.
在数据集 3, 5, 5, 7, 7, 7, 9 中，众数是 7，因为它出现了三次。
For 2, 2, 3, 3, 4, the modes are 2 and 3—this is called bimodal.
对于 2, 2, 3, 3, 4，众数为 2 和 3——这被称为双众数。
The mode is especially useful for non-numerical data, such as favourite colours or types of pet.
众数对于非数值数据尤其有用，例如最喜欢的颜色或宠物类型。
5. Understanding the Range | 理解极差
The range measures how spread out the data is. It is the difference between the largest and the smallest values.
极差衡量数据的分散程度。它是最大值与最小值之差。
Range = largest value − smallest value
极差 = 最大值 − 最小值
For the data 12, 7, 23, 5, 18, the largest is 23 and the smallest is 5, so range = 23 − 5 = 18.
对于数据 12, 7, 23, 5, 18，最大值为 23，最小值为 5，所以极差 = 23 − 5 = 18。
A small range means the data is quite consistent; a large range shows greater variation.
极差小意味着数据比较一致；极差大则显示变化较大。
6. Tally Charts and Frequency Tables | 计数图表与频率表
A tally chart is used to record data as it is collected, using tally marks (groups of five). A frequency table then shows the total count for each category.
计数图表用于在收集数据时用划记（每五条为一组）记录数据。频率表则显示每个类别的总数。
When constructing a frequency table, list all possible outcomes or categories, add the tally marks, and then write the frequency in the final column.
构建频率表时，列出所有可能的结果或类别，添加划记，然后在最后一列写出频数。
For example, a survey of favourite fruits might have categories ‘Apple’, ‘Banana’, ‘Orange’, with tally marks |||| for Apple, |||| || for Banana and ||| for Orange. The frequencies would be 4, 7 and 3.
例如，一项关于最喜欢水果的调查可能有类别“苹果”、“香蕉”、“橙子”，苹果的划记为 ||||，香蕉为 |||| ||，橙子为 |||。频数分别为 4、7 和 3。
7. Bar Charts | 条形图
A bar chart uses rectangular bars of equal width to represent data. The height of each bar corresponds to the frequency of that category. Bars should not touch each other for categorical or discrete data.
条形图使用等宽的矩形条来表示数据。每个条的高度对应于该类别的频数。对于分类或离散数据，条与条之间不应接触。
Always label the axes, give the chart a clear title, and use a consistent scale. The vertical axis usually shows frequency; the horizontal axis shows the categories.
务必标注坐标轴，为图表添加清晰的标题，并使用一致的刻度。纵轴通常显示频数；横轴显示类别。
Bar charts are ideal for comparing amounts, such as the number of students who prefer different sports.
条形图非常适合比较数量，例如喜欢不同运动的学生人数。
8. Pictograms | 象形图
A pictogram uses pictures or symbols to represent data. Each symbol stands for a certain number of items. A key is essential to explain what one symbol represents.
象形图使用图片或符号来表示数据。每个符号代表一定数量的项目。必须有图例来说明一个符号代表什么。
When drawing a pictogram, you may need to use half or part of a symbol to represent fractions of the amount shown by one symbol.
绘制象形图时，可能需要使用半个符号或部分符号来表示一个符号所代表数量的分数。
For instance, if one smiley face represents 4 students, then half a smiley face would represent 2 students.
例如，如果一个笑脸代表 4 名学生，那么半个笑脸就代表 2 名学生。
9. Pie Charts | 饼图
A pie chart is a circle divided into sectors, where each sector’s angle is proportional to the frequency it represents. The full circle is 360°.
饼图是一个被划分为扇形的圆，每个扇形的角度与其所代表的频数成比例。整个圆是 360°。
Angle = (frequency ÷ total frequency) × 360°
角度 = (频数 ÷ 总频数) × 360°
To draw a pie chart, first calculate the angle for each category, then use a protractor to mark the sectors. Label each sector or provide a legend.
绘制饼图时，先计算每个类别的角度，然后使用量角器标出扇形。标记每个扇形或提供图例。
Pie charts are excellent for showing proportions or percentages of a whole.
饼图非常适合显示整体中各部分的比例或百分比。
10. Line Graphs | 折线图
A line graph is used to show how data changes over time or in relation to another continuous variable. Points are plotted and then joined with straight lines.
折线图用于展示数据如何随时间变化或与另一个连续变量的关系。先描点，然后用直线连接。
Line graphs are ideal for showing trends, such as temperature changes over a day or the growth of a plant over several weeks.
折线图非常适合显示趋势，例如一天中温度的变化或几周内植物的生长。
Make sure the horizontal axis is labelled with the independent variable (often time) and the vertical axis with the dependent variable. Use a sensible scale that fits all the data.
确保横轴标注自变量（通常是时间），纵轴标注因变量。使用适合所有数据的合理刻度。
11. Discrete and Continuous Data | 离散数据与连续数据
Discrete data can only take certain values (often whole numbers) and is counted. Examples: number of students in a class, goals scored in a match, or the roll of a dice.
离散数据只能取特定的值（通常是整数），并且是计数得到的。例如：班级里的学生人数、比赛中的进球数或骰子的点数。
Continuous data can take any value within a range and is measured. Examples: height, weight, time, temperature, or the length of a leaf.
连续数据可以在一个范围内取任意值，
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