How does one handle ties in Order Statistics and Rank-Order Statistics? I'm preparing to calculate a data set's Mean Difference (equation given in the image below), but am having trouble understanding what I'm supposed to do when duplicate values are involved. My data consists of a large collection of integers which all have values in the set [0,5]. With such a small value set, ties are inevitable. However, I can't seem to find any resources that take this in to consideration. They all assume the probability of ties is 0 and continue with the material. Let's create a small example data set (bounded within the set of values that my actual data is): > [0, 3, 2, 5, 4, 4, 5, 1, 3, 5] How would one go about dealing with duplicates when calculating Order Statistic and Rank-Order Statistics? !enter image description here

There is no ambiguity at all. The order statistic in your example will simply be $$ [0,1,2,3,3,4,4,5,5,5], $$ that is $X_{(1)}=0$, $X_{(2)}=1$, $X_{(3)}=2$, $X_{(4)}=3$, $X_{(5)}=3$ and so on...