I'm looking for a way to characterize the deviation from a discrete uniform distribution.

Example: 50 balls are distributed over 10 urns.

In the most equal case, all urns get 5 balls. In the most unequal case, one urn gets all balls. Is there a (scalar) statistic that measures how equal things are distributed?

I thinking of something like the Gini index, but that does not quite fit in this scenario.

  • $\begingroup$ Why not just use the standard deviation? $\endgroup$
    – Lynn
    May 8 at 23:04
  • $\begingroup$ The discrete uniform maximizes entropy, so you can use entropy --- more generally, in ecology and other disiplines such measures are called measures of (bio)-diversity, there are many posts on this site! $\endgroup$ May 8 at 23:59
  • $\begingroup$ @cosine Start here en.wikipedia.org/wiki/Diversity_index $\endgroup$
    – Glen_b
    May 9 at 3:27