I don't really know the correct terminology to ask this question well. I have categorical data with counts and I want a measure of how "diverse" or "spread out" the data is. Variance comes to mind, but I don't know if that applies here.
Here is a two example of three distributions:
Sample 1 A: 100 B: 0 C: 0 Sample 2 A: 20 B: 20 C: 20
Things to note: the overall size between samples will not be consistent (i.e. how sample 1 has 100 counts and sample 2 has 60 counts) but I would like to compare between samples. In addition sample 1 and sample 2 represent opposite ends of the spectrum of the metric I would like where sample 2 is uniformly distributed (highly variant) and sample 1 has minimal variance. In addition the data is categorical so (A:10, B:0, C:10) should be equivalent to (A:0, B:10, C:10) when evaluated.
New Question: Within sample and between sample categorical variation