Problem:
A fifth number, , is added to the set of numbers to make the mean of the set of five numbers equal to its median. The number of possible values for is
Answer Choices:
A.
B.
C.
D.
E. more than
Solution:
There are three possible values for the new number, It is either less than , between and , or greater than . If the five elements are listed in increasing order, these three possibilities in the table below are: one of the first two, the middle one, and one of the last two. Since the median is the middle number in a set of five elements, there are three values for the median: , , or .
Query: Can you find the values of and which of the two alternatives occurs in the first and third cases?
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions