Which of these sets of five whole numbers has mean 8 and median 6?

A mean of 8 over five numbers demands a total of 40, and a median of 6 demands that the middle number, once the set is in order, is 6. Only 2, 4, 6, 8, 20 meets both: it totals 40 and its third value is 6. The set 2, 5, 9, 10, 14 also totals 40, so its mean is 8, but its middle value is 9. The set 3, 4, 6, 7, 10 has the required median 6, but totals 30 and so has mean 6. The set 4, 5, 7, 9, 10 totals 35 and has middle value 7, so it fails on both counts. Notice what the winning set looks like: to hold the median down at 6 while lifting the mean to 8 it needs one large value, 20, well away from the rest — a mean above the median is the usual sign of a set with a long tail to the right.