📚 Year 7 Edexcel Statistics: Quick Reference Handbook of Formulae and Theorems | Year 7 Edexcel 统计：公式定理速查手册
This quick reference handbook pulls together all the essential formulae, rules and theorems you will meet in the Year 7 Edexcel Statistics course. Keep it by your side when you are revising, tackling homework or preparing for assessments – everything is laid out in clear, paired English and Chinese explanations.
本速查手册汇集了你在 Year 7 Edexcel 统计课程中将会遇到的所有关键公式、规则和定理。复习、写作业或备考时把它放在手边——所有内容都以清晰的中英对照形式呈现。
1. Mean | 平均数
The mean is the most common measure of average. To find the mean, add all the data values together and then divide by how many values there are.
平均数是最常见的集中量数。求平均数需要先把所有数据值相加，然后除以数据的个数。
The formula for the mean is:
平均数的公式为：
Mean = Σx ÷ n
Here Σx stands for the sum of all the values, and n is the number of values.
其中 Σx 代表所有值的总和，n 是值的个数。
Example: For the data set 4, 7, 8, 9, the sum is 4+7+8+9 = 28, and n = 4, so Mean = 28 ÷ 4 = 7.
例如：对于数据集 4, 7, 8, 9，总和为 4+7+8+9 = 28，n = 4，因此平均数 = 28 ÷ 4 = 7。
2. Median | 中位数
The median is the middle value when the data are arranged in order from smallest to largest. It splits the data into two equal halves.
中位数是将数据从小到大排列后处于中间位置的值，它将数据分成数量相等的两半。
To find the position of the median, use:
查找中位数的位置，可使用：
Median position = (n + 1) ÷ 2
If n is odd, the median is the value at that exact position. If n is even, the median is the mean of the two middle values.
如果 n 为奇数，中位数就是该位置上的数值；如果 n 为偶数，中位数则是中间两个数值的平均数。
3. Mode | 众数
The mode is the value that appears most often in a data set. A set of data can have one mode (unimodal), two modes (bimodal) 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数值。一组数据可以有一个众数（单峰）、两个众数（双峰），或者当所有值都只出现一次时没有众数。
In a frequency table the mode is the category or value with the highest frequency.
在频数表中，众数就是频数最高的那个类别或数值。
4. Range | 极差
The range measures how spread out the data are. It is the difference between the largest value and the smallest value.
极差用于衡量数据的分散程度，它是最大值与最小值之间的差。
Range = Highest value – Lowest value
A larger range means the data are more spread out; a smaller range means they are more clustered together.
极差越大说明数据越分散，极差越小说明数据越集中。
5. Frequency Tables | 频数表
A frequency table shows how often each value or category occurs. It often includes a tally column to help count raw data.
频数表显示每个数值或类别出现的次数，通常包含一栏划记（tally）来帮助清点原始数据。
The frequency column records the count for each item. The sum of all frequencies always equals the total number of data points.
频数列记录每项出现的次数。所有频数的总和总是等于数据点的总数。
Σf = Total number of data values
6. Mean from a Frequency Table | 从频数表求平均数
When data are grouped in a frequency table, we multiply each value by its frequency (f × x), sum these products and then divide by the total frequency.
当数据以频数表形式呈现时，需要先把每个数值乘以其频数（f × x），求这些乘积的总和，再除以总频数。
Mean = Σ(f × x) ÷ Σf
Steps: 1) Add a column for f × x. 2) Find the sum of the f × x column. 3) Find the sum of the frequencies. 4) Divide the two sums.
步骤：1）增加一列 f × x；2）求出 f × x 列的总和；3）求出频数的总和；4）将两个总和相除。
7. Pie Charts | 饼图
A pie chart shows proportions of a whole. The size of each sector (the ‘slice’) is determined by the frequency of the category relative to the total frequency.
饼图展示各部分占整体的比例。每个扇区（“扇形”）的大小由该类别的频数相对于总频数确定。
To find the angle for a sector:
求扇区角度：
Angle = (Frequency ÷ Total frequency) × 360°
Always check that the angles add up to 360°. A protractor is used to draw the sectors accurately.
务必检查所有角度之和为 360°，绘制时用量角器准确画出各扇区。
8. Probability Basics | 概率基础
Probability measures how likely an event is to happen. It is calculated as:
概率衡量一个事件发生的可能性大小，计算公式为：
P(Event) = Number of favourable outcomes ÷ Total number of possible outcomes
Probabilities can be written as fractions, decimals or percentages. All probabilities lie between 0 and 1 inclusive.
概率可以用分数、小数或百分数表示。所有概率都在 0 和 1 之间（含 0 和 1）。
An outcome is favourable if it matches the event we are interested in.
如果某个结果符合我们关心的事件，则该结果就是有利结果（favourable outcome）。
9. The Probability Scale | 概率尺度
The probability scale helps us describe how likely events are. It runs from 0 (impossible) to 1 (certain).
概率尺度帮助我们描述事件发生的可能性，范围从 0（不可能）到 1（确定）。
Key points on the scale:
尺度上的关键点：
- 0 – Impossible (cannot happen) | 0 – 不可能（绝不会发生）
- ¼ (0.25) – Unlikely | ¼（0.25） – 不太可能
- ½ (0.5) – Even chance | ½（0.5） – 机会均等
- ¾ (0.75) – Likely | ¾（0.75） – 很可能
- 1 – Certain (will definitely happen) | 1 – 确定（一定会发生）
Words such as ‘even chance’, ‘fair’, ‘more likely’ and ‘less likely’ are often tested in Year 7.
Year 7 的阶段常会考察诸如“机会均等”、“公平”、“更可能”和“不太可能”等词语的正确使用。
10. Types of Data | 数据类型
Data can be classified into different types. Knowing the type helps us decide which charts and statistics to use.
数据可以分为不同类型，弄清数据类型有助于我们选择合适的图表和统计量。
Qualitative data describes qualities or categories (e.g. favourite colour, car brand). It is non-numerical. | 定性数据（Qualitative data） 描述性质或类别（如最喜欢的颜色、汽车品牌），是非数值型数据。
Quantitative data consists of numbers and can be measured (e.g. height, test scores). | 定量数据（Quantitative data） 由数字组成，可以被测量（如身高、测验分数）。
Quantitative data is further divided into:
定量数据进一步分为：
- Discrete data – can only take particular values, often whole numbers (e.g. number of books). Spanish: 离散数据 – 只能取特定值，通常是整数（如图书的数量）。
- Continuous data – can take any value within a range and is measured (e.g. mass, time). 连续数据 – 在某个范围内可以取任意值，来自测量（如质量、时间）。
11. Pictograms | 象形图
A pictogram uses pictures or symbols to represent data. Each picture stands for a certain number of items – this is called the key.
象形图用图片或符号来表示数据。每个图片代表一定数量的物品，这被称作图例（key）。
To read a pictogram correctly, always check the key first. If a picture represents 2 units, half a picture represents 1 unit.
要正确读取象形图，务必先查看图例。如果一个图片代表 2 个单位，则半个图片代表 1 个单位。
When drawing a pictogram, choose a key that makes the pictures easy to work with and label the axes clearly.
绘制象形图时，要选择一个便于操作的图例，并清晰地标注坐标轴。
12. Comparing Data Sets | 比较数据集
When comparing two sets of data, we often use an average (mean, median or mode) and the range.
比较两组数据时，我们通常使用一个平均数（均值、中位数或众数）和极差。
An average tells you about the typical value; the range tells you how consistent or spread out the data are.
平均数告诉你典型值是什么，极差则告诉你数据的一致性或分散程度。
For example, if set A has a higher mean than set B, set A tends to have larger values. If set B has a smaller range, it is more consistent.
例如，如果数据集 A 的平均数高于数据集 B，那么 A 的值通常更大；如果 B 的极差更小，则 B 的一致性更好。
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