Deriving median from minimum and range

Question

Let's say you have an odd number of n distinct integer and you know the range of these integers. (E.g. your min integer is 10 and your max integer is 50, this implies that the range is 30)

Is there a way to prove that that the median of these n distinct integers is the value with the smallest difference from the min+(range+2)/2?

Answer 1

This is clearly false. Consider $5$ distinct integers $1, 50, 51, 52, 53$ so range is $52$ and your median value is $1 + (52+2)/2 = 1+27 = 28$...