Question

The median of the list n, n + 2, n+3, n+5, n+7, n+8, n+11, n+14, n+16, n+19 is 20. What is the mean?

Answer 1

21

Explanation:

To find the median of the given set, you narrow the options down and get n+7 and n+8 as the middle numbers. The average of those two is n+7.5, so that's the median.

n+7.5=20

n=12.5

Substitute n into the values.

12.5, 14.5, 15.5, 17.5, 19.5, 20.5, 23.5, 26.5, 28.5 and 31.5.

Add everything together to get 210. Divide 210 by 10, the number of values, and you end up with 21.

Answer 2

16

Explanation:

The median is the average of n + 7 and n + 8 which is n + 7.5. This means that n + 7.5 = 20 so n = 12.5. The average (or mean) is the sum of terms divided by the number of terms. The sum is 10n + 85 and the number of terms is 10, We know that n = 7.5 so the answer is 10 * 7.5 + 85 / 10 = 75 + 85 / 10 = 160 / 10 = 16.