Find the standard deviation of the six numbers 4, 4, 4, 10, 10, 10.

The mean is 42 ÷ 6 = 7 and every observation lies exactly 3 away from it, so the variance is $(6\times 3^2)÷6=9$ and the standard deviation is √9 = 3. Answering 9 hands back the variance instead of its square root — the commonest slip of all. The value 6 is the range 10 − 4 and 4.5 is half that range, neither of which is a standard deviation.