The median for a set of 10 numbers is 10. An even number is added, and the median is now 11 and the range is now 4. What number was added?

Answer 1

If the numbers are x1-x10, then the median is

(x5 + x6)/2 = 10

Since the range was less than 4, that means that the numbers in order were

8 x x x 9 11 11 11 11 11
or
9 9 9 9 9 11 x x x 12 12

The median moved upward, so the even number was added on the top side, so it must have been 12.