Statistics 简明教程

Statistics - Grand Mean

当样本量相等时，换句话说，每个样本中可能有五个值，或每个样本中有 n 个值。总平均值与样本平均值的平均值相同。

When sample sizes are equal, in other words, there could be five values in each sample, or n values in each sample. The grand mean is the same as the mean of sample means.

Formula

其中——

Where −

  1. ${N}$ = Total number of sets.

  2. ${\sum x}$ = sum of the mean of all sets.

Example

Problem Statement:

Problem Statement:

确定每个组或组样本的平均值。使用以下数据作为样本以确定平均值和总平均值。

Determine the mean of each group or set’s samples. Use the following data as a sample to determine the mean and grand mean.

Jackson

1

6

7

10

4

Thomas

5

2

8

14

6

Garrard

8

2

9

12

7

Solution:

Solution:

步骤 1：计算所有均值

Step 1: Compute all means

步骤 2：将总和除以组数以确定总均值。在示例中，共有三个组。

Step 2: Divide the total by the number of groups to determine the grand mean. In the sample, there are three groups.