The mean of 20 numbers is 45. One of the numbers is increased by 60 and nothing else changes. By how much does the mean increase?

The total rises by 60 while the count stays at 20, so the mean rises by 60 ÷ 20 = 3, moving from 45 to 48. The whole 60 belongs to a single number and is shared out over all twenty, so quoting 60 as the change in the mean is twenty times too large. The values 6 and 0.6 divide by 10 and by 100 instead of by the actual count.