For the four numbers 2, 4, 6 and 8, by how much does the mean of their squares exceed the square of their mean?

Their mean is 20 ÷ 4 = 5, so the square of the mean is 25. Their squares are 4, 16, 36 and 64, which add to 120, so the mean of the squares is 120 ÷ 4 = 30. The excess is 30 − 25 = 5. That gap can never be negative, and it is exactly the variance of the data — a shortcut worth remembering. Answering 30 or 25 hands back one of the two quantities instead of their difference, and 95 uses the SUM of the squares, 120, where the mean of the squares belongs.