Problem:
The mean, median, and mode of the data values are all equal to . What is the value of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The mean of the data values is
Solving this equation for gives . Thus the data in nondecreasing order are , so the median is and the mode is , as required.
The problems on this page are the property of the MAA's American Mathematics Competitions