The grand mean is the mean

Mean

In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....

 of the means of several subsamples. For example, consider several lots, each containing several items. The items from each lot are sampled

Sampling (statistics)

In statistics and survey methodology, sampling is concerned with the selection of a subset of individuals from within a population to estimate characteristics of the whole population....

 for a measure

Measure

- Legal :* Measure of the Church of England is a law passed by the General Synod and the UK Parliament equivalent of an Act* Measure of the National Assembly for Wales, a law specific to Wales passed by the Welsh Assembly between 2007 and 2011...

 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.

Example

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

Standard deviation

Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...

. 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.