The grand mean is the mean of the means of several subsamples.[1] For example, consider several lots, each containing several items. The items from each lot are sampled for a measure of some variable and the means of the measurements from each lot are computed. The mean of the measures from each lot constitute the subsample mean. The mean of these subsample means is then the grand mean.
Bob is interested in determining which American states have the tallest people. To do so Bob measures the height of a suitably sized sample of individuals in each state, separating individuals into groups by gender. Next Bob calculates the respective means for each state, and finally the grand mean for each gender with the corresponding standard deviation. Now Bob has the necessary information for a preliminary determination of which states have abnormally tall or short individuals by comparing the means of each state to the grand mean ± the standard deviation.