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
XGM=∑xNXGM=∑xN
Where −
· NN = Total number of sets.
· ∑x∑x = sum of the mean of all sets.
Example
Problem Statement:
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:
Step 1: Compute all means
M1=1+6+7+10+45=285=5.6M2=5+2+8+14+65=355=7M3=8+2+9+12+75=385=7.6M1=1+6+7+10+45=285=5.6M2=5+2+8+14+65=355=7M3=8+2+9+12+75=385=7.6
Step 2: Divide the total by the number of groups to determine the grand mean. In the sample, there are three groups.
XGM=5.6+7+7.63=20.23=6.73
