You can use the Herfindahl-Hirschman Index (HHI) or other measures of entropy (e.g. Gini, Theil) for this. Based on your description, I think the former may be the easiest.

It is basically the sum of squared proportions of the identified categories. If column A(B) represents the number of observations from group A(B), the excell command should be something like "= (A1/(A1+B1))^2+(B1/(A1+B1))^2". A similar term is added for each additional group.

Do note that the score of the index varies between 1/N and one. In case you only have 2 groups the range of the index is minimum 0.5, so you may want to normalise it to fit within the requested 0-1 range.

Thanks! Tested this just now and works quite well. The only 'problem' is that outcomes rise very quickly. If 3 out of 20 observations are from one group, the outcome is already 0.51. I presume this is inherent to the HHI index?

HHI uses a quadratic as opposed to linear function which is responsible for quick rises when close to the maximum and minimal (zero) marginal increases at the minimum. Still, 3 out of 20 should result in a score of 0.745. I noticed a small error in my original response that I've addressed now.

I also sent you an e-mail with a prepared excell sheet displaying all scores (0-20). I hope this helps

In my case, want to use the Blau index to measure the hetrogeneity of the board of directors but I don't know the range of values that I can define as hetrogeneity and the the ones that are homogeneous. Is between 0.5-0.9 hetrogeneous and 0.1-0.49 homogeneous?