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__

__Formula__

XGM=∑xNXGM=∑xN

Where −

· NN = Total number of sets.

· ∑x∑x = sum of the mean of all sets.

__Example__

__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