Population standard deviation and the mean of squares of different datasets are given in 1-4 below. Compute the population mean of each dataset and arrange in descending order.

Population mean equals the square root of the mean of squares minus the variance, since variance is mean of squares minus mean squared.

Dataset three yields a mean of nine, dataset two yields eight, dataset four yields seven, and dataset one yields six.

Arranged in descending order these means give the sequence three, two, four, one.

Any order starting with dataset one or four misplaces the largest mean.

The reversed sequence two, one, three, four inverts the correct ranking entirely.

This uses the identity that variance equals the mean of squares minus the square of the mean.