Solved – How to measure diversity (dispersion) of a categorical variable

I have unemployment rates for 3 regions (North, Center, South).

The unemployment rate is defined by (number of unemployed ($u$)/ active population ($pa$)). The unemployment rate by region ($r$) is $frac{u_r}{pa_r}$.

Data: $u_{north} = 0.07, u_{center} = 0.04, u_{south} = 0.08$

How to measure diversity/dispersion/inequality of unemployment by region, knowing that the only known data are those employment rates. Note: the sum of the rates $neq 1$.

Hm. Are you looking to measure the diversity of each region? Or the diversity across the regions? If the former, I think you would need more than these three data points. If the latter, you could use a diversity index:

For example, assuming equal populations, the Simpson index (in economics, HHI) would be 0.0129.

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