Suppose that a sample of n observations is formed from k subsamples containing n1, . . . , nk observations (n1 + . . . + nk = n). Let xij (j = 1, . . . , ni) denote the observations in the ith subsample, and let i + and v2i denote the sample mean and the sample variance of that subsample:

Finally, let ++ and v2 denote the sample mean and the sample variance of the entire sample of n observations:

Determine an expression for v2 in terms of ++, i+, and v2i (i = 1, . . . , k).

Mi ij )2 j-1 2 j-1 k ni ij++