I am studying a set of uniformly generated points, more concretely the distance between the points.
When the set is unsorted the histrogram shows it is normally distributed and that matches my intuition:
However, when the set is sorted the histogram resembles an exponential distribution:
The way my intuition works this means that the most common distance between 2 consecutive endpoints is the smallest one of all the distances which seems odd to me, my intuition when looking at the problem was driving me more towards an inverse-gaussian, I understand the most common distances will be close to the bottom but I was not expecting it to be straight the smallest one.
What property of this system makes this happen?