The grand mean is the mean of the means of several subsamples, as long as the subsamples have the same number of data points. 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 constitutes the subsample mean. The mean of these subsample means is then the grand mean.
Suppose one wishes to determine which American states have the tallest men. To do so one measures the height of a suitably sized sample of men in each state. Next one calculates the means for each state, and finally the grand mean (the mean of the state means) as well as the corresponding standard deviation of the state means. Now one has the necessary information for a preliminary determination of which states have abnormally tall or short men by comparing the means of each state to the grand mean ± some multiple of the standard deviation.
- Everitt, B.S. (2002) Cambridge Dictionary of Statistics (2nd Edition), CUP. ISBN 0-521-81099-X