📚 Year 7 WJEC Statistics: Quick Reference Formula & Theorem Handbook | WJEC 七年级统计：公式定理速查手册
This quick-reference handbook brings together the most important formulas, definitions and theorems from the Year 7 WJEC Statistics course. Each section is presented in a clear, bilingual format, with step-by-step examples to help you revise quickly and confidently.
本速查手册汇集了 WJEC 七年级统计课程中最重要的公式、定义和定理。每个部分都以清晰的双语形式呈现，并配有分步示例，帮助你快速自信地复习。
1. Types of Data | 数据类型
Discrete data can only take specific values, typically whole numbers, and is counted. Examples include the number of students in a class or the score on a dice roll.
离散数据只能取特定的值，通常是整数，并可通过计数得到。例如班级里的学生人数或者掷骰子的点数。
Continuous data can take any value within a given range and is measured. Examples include height, weight, temperature and time.
连续数据可以取某个范围内的任意值，并通过测量得到。例如身高、体重、温度和时间。
2. Mean (Average) | 平均数
The arithmetic mean is the sum of all data values divided by the number of values. It is the most commonly used average.
算术平均数是所有数据值之和除以数据值的个数。这是最常用的平均数。
Mean = Σx ÷ n
where Σx represents the sum of all data values and n is the number of values.
其中 Σx 表示所有数据值之和，n 表示数据值的个数。
Example: For the numbers 4, 7, 9, 6 and 8, the mean is (4+7+9+6+8) ÷ 5 = 34 ÷ 5 = 6.8.
示例：对于数字 4、7、9、6 和 8，平均数为 (4+7+9+6+8) ÷ 5 = 34 ÷ 5 = 6.8。
3. Median | 中位数
The median is the middle value when the data is arranged in order (smallest to largest). If there is an odd number of values, the median is the central one. If there is an even number, it is the mean of the two central values.
中位数是将数据从小到大排序后位于中间的值。如果数据个数为奇数，中位数就是正中间那个数；如果为偶数，则是中间两个数的平均数。
Example: The ordered data set 3, 5, 7, 9, 12 has median 7. The ordered set 2, 4, 6, 8 has median (4+6) ÷ 2 = 5.
示例：有序数据集 3、5、7、9、12 的中位数为 7。有序集 2、4、6、8 的中位数为 (4+6) ÷ 2 = 5。
4. Mode (Modal Value) | 众数
The mode is the value that appears most frequently in a data set. A set may have one mode, more than one mode (called bimodal or multimodal), or no mode if all values occur equally often.
众数是数据集中出现次数最多的数值。一组数据可能只有一个众数，也可能有多个众数（称为双众数或多众数），如果所有值出现次数相同则没有众数。
Example: In the set 2, 3, 3, 5, 5, 5, 8, the mode is 5. In 1, 1, 2, 2, there are two modes (1 and 2).
示例：在集合 2, 3, 3, 5, 5, 5, 8 中，众数是 5。在 1, 1, 2, 2 中，有两个众数（1 和 2）。
5. Range | 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间的差值。
Range = Maximum value – Minimum value
Example: In the data set 12, 7, 19, 3, 9, the maximum is 19 and the minimum is 3, so the range is 19 – 3 = 16.
示例：数据集 12、7、19、3、9 中，最大值为 19，最小值为 3，因此极差为 19 – 3 = 16。
6. Mean from a Frequency Table | 频数表求平均数
When data is organised in a frequency table, the mean can be found by multiplying each data value by its frequency, summing these products, and dividing by the total frequency.
当数据用频数表整理时，可以通过将每个数据值乘以其频数、求乘积之和，再除以总频数来计算平均数。
Mean = Σ(f × x) ÷ Σf
where f is the frequency and x is the data value.
其中 f 为频数，x 为数据值。
Example: A table shows score 1 (frequency 3), score 2 (freq 5), score 3 (freq 2). Σ(f×x) = 1×3 + 2×5 + 3×2 = 3+10+6 = 19. Σf = 10. Mean = 19 ÷ 10 = 1.9.
示例：表格显示得分 1（频数 3）、得分 2（频数 5）、得分 3（频数 2）。Σ(f×x) = 1×3 + 2×5 + 3×2 = 3+10+6 = 19。Σf = 10。平均数 = 19 ÷ 10 = 1.9。
7. Bar Charts | 条形图
A bar chart uses rectangular bars of equal width to display frequencies. The category is shown on the horizontal axis, and the frequency on the vertical axis. The height of each bar represents the frequency for that category.
条形图使用等宽的矩形条显示频数。横轴显示类别，纵轴显示频数。每个条形的高度代表该类别的频数。
Bars are usually separated by equal gaps. The chart must have a title, labelled axes and an appropriate scale.
各条形之间通常留有相等间隙。图表必须有标题、带标签的坐标轴和合适的刻度。
Example: A bar chart of favourite colours with frequencies: Red 8, Blue 12, Green 5 will show three bars of heights 8, 12 and 5.
示例：最喜爱颜色的条形图，频数分别为红色 8、蓝色 12、绿色 5，将显示三条高度为 8、12 和 5 的条形。
8. Pie Charts | 饼图
A pie chart is a circle divided into sectors, each representing
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