A pupil claims that when choosing an average, only unusually large values can distort the result. The data set 2, 40, 41, 42 and 45 has a mean of 34 and a median of 41. Which average does the single small value 2 pull away from the bulk of this data?

Explanation

The five values total 170, so the mean is 34, which is six below even the smallest of the four values clustered between 40 and 45, while the middle value of 41 stays inside that cluster. A small value lowers a total in the same way a large value raises it, so the pupil's claim is wrong, and the average built from the total is the one that ends up outside the group.