ACT Question of the Day #38

Ms. Hernandez began her math class by saying:  I’m thinking of 5 numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14, what is the 5th number?

What is the 5th number Ms. Hernandez is thinking of?

A.  13
B.  14
C.  15
D.  16
E.  18


The answer is:   E.  18

Since there will be an odd number of terms, the median will have to be the middle number. Write out the numbers in the original set in numerical order. You will see no matter where you place the 5th term, the median will be 14. Ms. Hernandez said that the mean is equal to the median, so the mean is also going to be 14. If x = the 5th number, then the mean is 14 = . So, 14(5) = 52 + x, or x = 18.