The difference between two consecutive odd or even numbers would be 2.
We let the first term be x, then x+2, x+4, x+6, x+8
= [5x + 20] / 5
= x + 4 which is the middle term
In order to make it easier we would represent it by x-4, x-2, x , x+2, x+4
[x-4 + x-2 + x + x+2 + x+4] / 5
Therefore the average is the middle term.