📚 Year 7 OCR Statistics: Formula & Theorem Quick Reference | 七年级OCR统计：公式定理速查手册
This handbook pulls together every key formula, method and concept you will meet in the Year 7 OCR Statistics course. Treat it as your quickfire revision companion – all the essentials in one place, with worked examples to help you remember.
这本手册汇集了七年级OCR统计课程中您将遇到的所有关键公式、方法和概念。您可以把它当作快速复习的伙伴——所有要点汇聚一处，并配有解题示例帮助您记忆。
1. Types of Data | 数据类型
Data can be split into qualitative data and quantitative data. Qualitative data describes qualities, labels or categories that cannot be measured with numbers, such as hair colour, favourite sport or types of pet.
数据可以分为定性数据和定量数据。定性数据描述无法用数字测量的性质、标签或类别，例如头发颜色、最喜欢的运动或宠物类型。
Quantitative data is numerical and can be measured or counted. It is further divided into discrete data (can only take certain values, e.g. number of siblings) and continuous data (can take any value in a range, e.g. height or time).
定量数据是数值型的，可以进行测量或计数。它进一步分为离散数据（只能取特定值，如兄弟姐妹的数量）和连续数据（可取一个范围内的任何值，如身高或时间）。
2. Frequency Tables | 频率表
A frequency table organises raw data by listing each different value alongside the number of times it appears – its frequency. The total frequency equals the number of data items.
频率表通过列出每个不同的值及其出现的次数（即频数）来整理原始数据。总频数等于数据项的数量。
| Number of pets (x) | Frequency (f) |
|---|---|
| 0 | 4 |
| 1 | 8 |
| 2 | 5 |
| 3 | 3 |
Always check that the frequencies add up to the total number of items you collected. This simple check prevents counting mistakes.
一定要检查频数之和是否等于您收集到的数据项总数。这个简单的核对能防止计数错误。
3. The Mean | 均值
The mean is the most common measure of average. To calculate it, add up every data value and then divide by the number of values.
均值是最常用的平均数度量。计算方法为：将所有数据值相加，再除以数据的个数。
Mean = (Sum of all data values) ÷ (Number of data values)
均值 = （所有数据值的总和） ÷ （数据值的个数）
Example: The heights of four plants are 12 cm, 15 cm, 10 cm and 19 cm. The sum is 12+15+10+19 = 56 cm. There are 4 values, so the mean height = 56 ÷ 4 = 14 cm.
示例：四株植物的高度分别为12厘米、15厘米、10厘米和19厘米。总和为12+15+10+19=56厘米。共有4个值，因此平均高度 = 56 ÷ 4 = 14厘米。
4. The Median | 中位数
The median is the middle value when the data are placed in order from smallest to largest. It splits the data set into two equal halves.
中位数是将数据从小到大排列后位于中间的值。它将数据集分成相等的两部分。
If there is an odd number of values (n), the median is the value at position (n+1)/2. For example, with 7 ordered numbers, the median is the 4th value.
如果数据个数 (n) 为奇数，中位数位于第(n+1)/2个位置。例如，有7个有序数，中位数就是第4个值。
If there is an even number of values, the median is the mean of the two middle values – those at positions n/2 and (n/2)+1. For 8 numbers, take the average of the 4th and 5th values.
如果数据个数为偶数，中位数是中间两个值（位于第n/2和(n/2)+1个位置）的均值。例如有8个数时，取第4和第5个值的平均数。
5. The Mode | 众数
The mode (or modal value) is the value that appears most often in a data set. A set of data may have one mode, more than one mode (bimodal or multimodal) or no mode if all values appear equally often.
众数（模态值）是数据集中出现次数最多的值。一组数据可能有一个众数、多个众数（双众数或多众数），或者如果所有值出现的次数相同，则没有众数。
The mode is the only average that can be used for qualitative data. For example, if the most common eye colour in a class is brown, then brown is the mode.
众数是唯一可用于定性数据的平均数。例如，如果班级中最常见的眼睛颜色是棕色，那么棕色就是众数。
6. The Range | 范围
The range measures how spread out the data are. It is the difference between the largest and smallest values.
范围衡量数据的分散程度。它是最大值与最小值之间的差。
Range = Largest value − Smallest value
范围 = 最大值 − 最小值
A larger range means the data are more spread out; a smaller range means they are more consistent. The range is quick to calculate but can be affected by extreme values.
范围越大说明数据越分散；范围越小说明数据越一致。范围计算快捷，但容易受到极端值的影响。
7. Bar Charts and Pictograms | 条形图和象形图
A bar chart uses bars of equal width to represent frequencies or amounts for different categories. The height of each bar shows the frequency – there are gaps between the bars because the categories are separate.
条形图使用宽度相等的条形来表示不同类别的频数或数量。每个条形的高度代表频数——条形之间留有空隙，因为各类别是分开的。
Every bar chart must have a title, clearly labelled axes and a sensible scale. The scale on the frequency axis should start at zero and go up in equal steps.
每个条形图都必须有标题、清晰的坐标轴标签和合理的刻度。频数轴上的刻度应从零开始，并以相等的步长递增。
A pictogram uses symbols or pictures to represent a certain number of items. A key tells you what one symbol stands for. When a frequency is not a multiple of the symbol value, part of a symbol is used.
象形图使用符号或图片来表示一定数量的项目。图例会告诉您一个符号代表什么。当频数不是符号值的倍数时，会使用部分符号。
8. Pie Charts | 饼图
A pie chart displays data as slices of a circle. The size of each slice (sector angle) is proportional to the frequency of that category. The total of all frequencies corresponds to 360°.
饼图以圆形的扇区显示数据。每个扇区的大小（扇形角）与该类别的频数成正比。所有频数的总和对应360°。
Sector angle = (Frequency of category ÷ Total frequency) × 360°
扇形角 = （类别频数 ÷ 总频数） × 360°
Example: In a survey of 30 students about transport to school, 12 walk. The angle for ‘walk’ is (12 ÷ 30) × 360° = 0.4 × 360° = 144°. Always check that all sector angles sum to 360°.
示例：在一项对30名学生上学交通方式的调查中，12人步行。’步行’的扇形角为 (12 ÷ 30) × 360° = 0.4 × 360° = 144°。一定要检查所有扇形角之和是否为360°。
9. Line Graphs | 折线图
Line graphs are used to show how a quantity changes over time or across ordered categories. Points are plotted for each data pair and joined by straight lines to reveal trends.
折线图用于展示一个量如何随时间或有序类别而变化。在每对数据对应的位置描点，然后用直线连接，以显示趋势。
The horizontal axis usually shows time or the independent variable, and the vertical axis shows the quantity being measured. Make sure both axes are labelled and the graph has a clear title.
横轴通常表示时间或自变量，纵轴表示被测量的量。确保两条坐标轴都有标签，并且图表有清晰的标题。
A line graph can show upward trends, downward trends or periods where the value stays roughly the same. Reading between plotted points is called interpolation.
折线图可以显示上升趋势、下降趋势或数值大致保持不变的时期。在描点之间进行读取称为内插。
10. Introduction to Probability | 概率入门
Probability measures how likely an event is to happen. It always lies between 0 (impossible) and 1 (certain). It can be written as a fraction, a decimal or a percentage.
概率衡量一个事件发生的可能性大小。它始终介于0（不可能）与1（必然）之间。概率可以用分数、小数或百分数表示。
Probability of an event = Number of favourable outcomes ÷ Total number of possible outcomes
事件的概率 = 有利结果的数量 ÷ 所有可能结果的总数
Example: When rolling a fair six‑sided dice, the probability of getting an even number is 3/6 = 1/2, because there are 3 favourable outcomes (2, 4, 6) out of 6 possible outcomes.
示例：掷一个公平的六面骰子时，获得偶数的概率是3/6 = 1/2，因为在6种可能的结果中有3种有利结果（2、4、6）。
If an experiment is repeated many times, the relative frequency of an event should get closer to its theoretical probability. This is called the law of large numbers.
如果重复进行无数次实验，一个事件的相对频率应当趋近于它的理论概率。这称为大数定律。
11. Mean from a Frequency Table | 频率表中的均值
When data are summarised in a frequency table, you can still find the mean. Multiply each data value by its frequency, add all those products, then divide by the total frequency.
当数据用频率表汇总时，您仍然可以求均值。将每个数据值乘以其频数，将所有乘积相加，再除以总频数。
Mean = (Sum of (each value × its frequency)) ÷ (Total frequency)
均值 = （每个值 × 其频数的和） ÷ （总频数）
Using the earlier pets frequency table (0, 1, 2, 3 with frequencies 4, 8, 5, 3): the sum of (value × frequency) is (0×4)+(1×8)+(2×5)+(3&
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