Problem:
A student attempted to compute the average, , of , and by computing the average of and , and then computing the average of the result and . Whenever , the student's final result is
Answer Choices:
A. correct
B. always less than
C. always greater than
D. sometimes less than and sometimes equal to
E. sometimes greater than and sometimes equal to
Solution:
The true average is . The student computed
Thus
which is always positive since and .
Note. In effect, the student averaged the four numbers . Since the largest number was counted twice, the student's average is larger than the average of .