A Quick Reference Handbook of Formulas and Theorems for Year 8 SQA Statistics | Year 8 SQA 统计：公式定理速查手册

📚 A Quick Reference Handbook of Formulas and Theorems for Year 8 SQA Statistics | Year 8 SQA 统计：公式定理速查手册

This quick reference handbook contains all the key formulas, definitions and theorems you need for Year 8 SQA Statistics. It is designed to help you revise and quickly look up important concepts before tests.

本速查手册涵盖了 Year 8 SQA 统计学所有关键的公式、定义和定理，帮助你在考试前进行高效复习和快速查阅。

1. Mean | 平均数

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

平均数（或平均值）是一种集中量数。计算方法是先将所有数据值相加，再除以数据值的总个数。

If a data set contains n values, listed as x₁, x₂, …, xₙ, then the mean is given by the formula:

如果数据集包含 n 个值，记为 x₁, x₂, …, xₙ，则平均数由以下公式给出：

Mean = (x₁ + x₂ + … + xₙ) ÷ n

For example, the mean of 4, 7, 9, 10 is (4+7+9+10)÷4 = 30÷4 = 7.5.

例如，数据集 4、7、9、10 的平均数为 (4+7+9+10)÷4 = 30÷4 = 7.5。

2. Median | 中位数

The median is the middle value when the data are arranged in order. It splits the data into two equal halves.

中位数是一组数据排序后位于中间位置的数值，它将数据分成相等的两部分。

To find the median: first order the numbers from smallest to largest. If there is an odd number of values, the median is the middle one. If there is an even number of values, the median is the mean of the two middle numbers.

求中位数的步骤：先将数据从小到大排列。如果数据个数为奇数，则中位数为最中间的那个数；如果个数为偶数，则中位数为中间两个数的平均数。

Example: For the data 3, 5, 7, the median is 5. For 2, 4, 6, 8, the median is (4+6)÷2 = 5.

示例：数据集 3、5、7 的中位数是 5。数据集 2、4、6、8 的中位数是 (4+6)÷2 = 5。

3. Mode | 众数

The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, 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数值。一组数据可能有一个众数、多个众数，或者如果没有数值重复出现，则没有众数。

For example, in the list 2, 3, 3, 5, 7, the mode is 3. In 1, 2, 2, 4, 4, 6, the modes are 2 and 4 (bimodal).

例如，在数据集 2、3、3、5、7 中，众数是 3。在 1、2、2、4、4、6 中，众数为 2 和 4（双众数）。

4. Range | 极差

The range is a measure of spread. It shows how spread out the data values are. It is calculated as the difference between the largest and smallest values.

极差是用来

Published by TutorHao | Year 8 统计 Revision Series | aleveler.com

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