Samuelson’s inequality (also attributed to K. R. Nair) gives a bound on the extremes in a sample in terms of the mean and variance:                  |xi − ¯x| ≤ s √ n − 1. Use this to bound the...

Samuelson’s inequality (also attributed to K. R. Nair) gives a bound on the extremes in a sample in terms of the mean and variance:

                 |xi − ¯x| ≤ s √ n − 1.

Use this to bound the cancellation in (2.5.1) by giving a bound on the ratio

                n(x1 − ¯x)2 (xi − x1) 2 .