Suppose ten distinct, positive integers have a median of 10. ("Distinct integers" means that no two integers are the same.)

What is the smallest possible average of those ten integers?

Guest Apr 25, 2022

#2**+1 **

Since the median is ten and there are ten distinct numbers, the median must be found by finding the mean between the two "middle" numbers.

This could be done by having the integers 9 and 11 in the group.

The four smallest numbers less than 9 are 1, 2, 3, and 4.

The four smallest numbers more than 11 are 12, 13, 14, and 15.

My guess is that the set consists of 1, 2, 3, 4 9, 11, 12, 13, 14, and 15.

geno3141 Apr 25, 2022