OK, young person! Here is my attempt at this:
Here are ALL 3-digit numbers in base 5, which are 2-digit numbers in base 8:
100, 101, 102, 103, 104, 110, 111, 112, 113, 114, 120, 121, 122, 123, 124, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144. If you count them you should get 25 such numbers. And their average is: [100 + 144] /2 = 122 in base 5, which is the exact median of the above list. Converting [100 + 144] / 2 =122 from base 5 to base 10, you get: [25 + 49] / 2 =37 in base 10.