Care for a test of mathematical intuition?

I confess that I was not able to intuit the answer to this problem, but I will state it in such a way as to encourage looking at it in the right way.

First consider this easy problem. Randomly select numbers from 0 to 60. What will be the average value of the selected numbers? It should be reasonable that the average will tend to be the middle number, 30.

Now randomly choose two numbers at a time from 0 to 60. Keep track separately of the smaller of the two numbers and the larger of the two numbers. What will be the average of the smaller numbers and what will be the average of the larger numbers?