To find the median of a set of numbers, we need to first arrange the numbers in order from smallest to largest.
1, 1, 3, 3, 4, 5, 7, 7
There are 8 numbers in the set, which is an even number. In this case, the median is the average of the two middle numbers.
The two middle numbers are 3 and 4, so the median is (3 + 4) / 2 = 3.5.
Therefore, the median of the set {1, 3, 1, 3, 1, 7, 4, 5, 7} is 3.5.