In which set of scores is the median greater than the mean?
(A) $10,20,40,40,40$
(D) $10,20,30,100,200$
(B) $40,50,60,70,80$
(C) $20,20,20,50,80$
Solution 1

Since the scores in each of the 5 sets are listed in order, from smallest to largest, the number in the middle (the 3rd number) of the 5 numbers is the median.

The mean is calculated and also shown below for each of the 5 sets of scores.

| Set of Scores | Median | Mean |
| :---: | :---: | :---: |
| $10,20,40,40,40$ | 40 | $\frac{10+20+40+40+40}{5}=\frac{150}{5}=30$ |
| $40,50,60,70,80$ | 60 | $\frac{40+50+60+70+80}{5}=\frac{300}{5}=60$ |
| $20,20,20,50,80$ | 20 | $\frac{20+20+20+50+80}{5}=\frac{190}{5}=38$ |
| $10,20,30,100,200$ | 30 | $\frac{10+20+30+100+200}{5}=\frac{360}{5}=72$ |
| $50,50,50,50,100$ | 50 | $\frac{50+50+50+50+100}{5}=\frac{300}{5}=60$ |

From the table above, we see that the first set of scores is the only set in which the median, 40 , is greater than the mean, 30 .

## Solution 2

The first set of 5 scores, 10, 20,40,40,40, is ordered from smallest to largest and thus the median is the 3rd (middle) number of this set, 40.

The mean of the final 3 numbers of this set is also 40 , since each is equal to 40 .

Since the first 2 numbers of the set are both less than the mean of the other 3 numbers (40), then the mean of all 5 numbers in the set must be less than 40 .

Using a similar argument for the remaining four answers, we see that each of the other four sets has its mean equal to or greater than its median.

Therefore, the first set of scores is the only set in which the median is greater than the mean.

ANSWER: (A)