Year 7 CAIE Statistics: Formula and Key Concept Quick Reference Handbook | 7年级CAIE统计：公式定理速查手册

📚 Year 7 CAIE Statistics: Formula and Key Concept Quick Reference Handbook | 7年级CAIE统计：公式定理速查手册

This quick reference handbook provides Year 7 students following the CAIE curriculum with a concise summary of all essential statistical formulas, definitions, and graphical representations. It covers measures of central tendency (mean, median, mode), measures of spread (range), data handling tools (frequency tables, bar charts, pictograms, pie charts, line graphs), and the fundamentals of probability. Use this guide to revise key concepts quickly and confidently.

本速查手册为学习CAIE课程的7年级学生提供了所有重要统计公式、定义和图表表示的简明总结。涵盖集中趋势的度量（平均数、中位数、众数）、离散程度的度量（极差）、数据处理工具（频数表、条形图、象形图、饼图、折线图）以及概率基础。使用本指南可以快速、自信地复习关键概念。

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1. Mean (Average) | 平均数

The mean (often called the average) is a measure of central tendency. It is found by adding together all the values in a data set and then dividing by the total number of values.

平均数（通常称为平均值）是一种集中趋势的度量。它的计算方法是将数据集中所有数值相加，然后除以数值的总个数。

The mean is useful for comparing data sets but can be affected by extremely high or low values (outliers).

平均数对于比较数据集很有用，但会受到极大或极小值（异常值）的影响。

Formula: Mean = (Sum of all data values) ÷ (Number of data values)

公式：平均数 = (所有数据值之和) ÷ (数据个数)

If we use the symbol Σ (sigma) to represent ‘sum of’, and n for the number of values, we can write: Mean = Σx / n.

如果使用符号Σ（西格玛）表示“总和”，n表示数值的个数，则可以写作：平均数 = Σx / n。

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2. Median | 中位数

The median is the middle value when a data set is arranged in order from smallest to largest.

中位数是将数据集从小到大排列后，位于中间位置的数值。

If there is an odd number of data values, the median is simply the middle number. If there is an even number of values, the median is the mean of the two middle numbers.

如果数据值的个数是奇数，中位数就是正中间的那个数。如果数据值的个数是偶数，中位数是中间两个数的平均数。

The median is not affected by outliers and is often used for skewed data, such as house prices or incomes.

中位数不受异常值影响，常用于偏斜数据，如房价或收入。

Example: For the set 3, 5, 7, 9, 12, the median is 7. For the set 3, 5, 7, 9, the median is (5+7)/2 = 6.

示例： 对于数据集 3, 5, 7, 9, 12，中位数是 7。对于数据集 3, 5, 7, 9，中位数是 (5+7)÷2 = 6。

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3. Mode | 众数

The mode is the value that appears most frequently in a data set. There can be one mode (unimodal), two modes (bimodal), or no mode at all if all values occur equally often.

众数是数据集中出现次数最多的值。可能有一个众数（单峰）、两个众数（双峰），或者如果所有值出现次数相同则没有众数。

The mode is the only measure of central tendency that can be used with non-numerical (categorical) data, such as favourite colours or types of pets.

众数是唯一可用于非数值型（分类）数据的集中趋势度量，例如最喜欢的颜色或宠物种类。

In a frequency table, the mode is the value with the highest frequency.

在频数表中，众数是频数最高的那个值。

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4. Range | 极差

The range is a simple measure of spread or dispersion. It tells us how spread out the data values are.

极差是一种简单的离散程度或分散度量。它告诉我们数据值分布的广度。

Formula: Range = Maximum value − Minimum value

公式：极差 = 最大值 − 最小值

To find the range, subtract the smallest data value from the largest. The larger the range, the more spread out the data is.

要计算极差，用最大的数据值减去最小的数据值。极差越大，数据越分散。

The range is easily affected by outliers, so it should be used together with other measures.

极差容易受异常值影响，所以应当与其他度量一起使用。

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5. Frequency Tables | 频数表

A frequency table is a way of organising data to show how often each value or group of values occurs. It usually has columns for the data value (or class interval) and the frequency.

频数表是一种整理数据的方式，用来显示每个值或每组值出现的次数。它通常包含数据值（或组距）和频数两列。

Frequency tables help us to summarise large sets of data and make it easier to calculate statistics like the mode and mean.

频数表帮助我们汇总大量数据，并使得计算众数和平均数等统计量更容易。

When data is grouped into intervals (e.g., 0–10, 11–20), we call it a grouped frequency table. In Year 7, you may work with simple ungrouped frequency tables.

当数据被分到区间（例如0–10，11–20）时，我们称之为分组频数表。在7年级，你可能使用简单的未分组频数表。

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6. Mean from a Frequency Table | 从频数表计算平均数

If you have a frequency table, you can calculate the mean by multiplying each value by its frequency, summing these products, and then dividing by the total frequency.

如果有一个频数表，你可以通过将每个值乘以其频数，求和这些乘积，然后除以总频数来计算平均数。

Mean = Σ(f × x) ÷ Σf

平均数 = Σ(f × x) ÷ Σf

where f represents the frequency of each value and x is the data value. Σf is the total number of data items.

其中 f 表示每个值的频数，x 是数据值。Σf 是数据项的总数。

For example, if a table shows the number of pets: 0 pets (freq 4), 1 pet (freq 6), 2 pets (freq 2), then the mean number of pets

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