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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

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up vote 2 down vote accepted

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...

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