The intersecting chords theorem states that whenever two chords intersect, the product of their pieces is constant.
So, in this case, we have
Plugging your values, we have
This equation has solutions 
, but we can't choose 
, because it would lead to
So, the only feasible solutions is 
The answer is 35 7/8. We know that to get the mean, you must add up all the numbers and divide by the amount of numbers. Set up the equation (36 3/4 +36 3/8+37 1/2+n)/4 = 36 5/8. After you solve for n, the missing number, you should get 35 7/8.
Change 1/4 to a decimal is an exponent by 4 and the answer would be 0.0039
