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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
${X_{GM} = frac{sum x}{N}}$
Where −
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${N}$ = Total number of sets.
-
${sum x}$ = 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
$ {M_1 = frac{1+6+7+10+4}{5} = frac{28}{5} = 5.6 \[7pt]
, M_2 = frac{5+2+8+14+6}{5} = frac{35}{5} = 7 \[7pt]
, M_3 = frac{8+2+9+12+7}{5} = frac{38}{5} = 7.6 }$
, M_2 = frac{5+2+8+14+6}{5} = frac{35}{5} = 7 \[7pt]
, M_3 = frac{8+2+9+12+7}{5} = frac{38}{5} = 7.6 }$
Step 2: Divide the total by the number of groups to determine the grand mean. In the sample, there are three groups.
$ {X_{GM} = frac{5.6+7+7.6}{3} = frac{20.2}{3} \[7pt]
, = 6.73 }$
, = 6.73 }$
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