By | May 5, 2019

# Statistics – Grand Mean

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 −

• \${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 Thomas Garrard 1 6 7 10 4 5 2 8 14 6 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 }\$

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 }\$

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