Problem Solving

LUANDATO wrote:The median is larger than the average for which one of the following sets of integers?

(A) {8, 9, 10, 11, 12}
(B) {8, 9, 10, 11, 13}
(C) {8, 10, 10, 10, 12}
(D) {10, 10, 10, 10, 10}
(E) {7, 9, 10, 11, 12}

The OA is E.

I don't have it clear. Can any expert explain this PS question please? Thanks.

(A) {8, 9, 10, 11, 12}: This is an equally spaced set, thus the median = the average = 10
(B) {8, 9, 10, 11, 13}: We have median = 10. The first four terms are equally spaced, but the 5th one is '1' more than '12'. Thus, the average would be (13 - 12)/5 = 1/5 greater than the median.
(C) {8, 10, 10, 10, 12}: We have median = 10. The middle three terms are the same, but the 1st one is '2' less than 10 and the 5th one is '2' more than '12'. Thus, the average = median.
(D) {10, 10, 10, 10, 10}: The median = the average = 10
(E) {7, 9, 10, 11, 12}: We have median = 10. The last four terms are equally spaced, but the 1st one is '1' less than '8'. Thus, the average would be (8 - 7)/5 = 1/5 less than the median. The correct answer.

The correct answer: E

Hope this helps!

-Jay

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