Problem: For the numbers , e define to be the arithmetic mean of all five numbers; to be the arithmetic mean of and to be the arithmetic mean of , and ; and to be the arithmetic mean of and . Then, no matter how , e are chosen, we shall always have:
Answer Choices:
A.
B.
C.
D.
E. none of these
Solution:
From the given information , and If so that ; if , then ; if , then .
Since, for random selections of , it is possible for to equal, to be greater than, or to be less than , so it follows that can be cqual, can be greater than, or can be less than .