The items from each lot are sampled for a measure of some variable and the means of the measurements from each lot are computed.
[2] Suppose one wishes to determine which states in America have the tallest men.
To do so, one measures the height of a suitably sized sample of men in each state.
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.
In ANOVA, there is a similar usage of grand mean to calculate sum of squares (SSQ), a measurement of variation.
If the sample sizes across the G groups are equal, then the two statistics coincide.