Index of qualitative variation

Expressed as a ratio from 0 to 1.00.   Observed in a distribution of scores to the maximum variation that could exist in a particular distribution.

 0.00 indicates no variation.  1.00 represents maximum variation.

 The most common usage for this is for nominal variables and it can be used with any variable when scores have been grouped into a frequency distribution.

For example, given the following tables representing a city's marital status in the hundreds, we may want to know which of the two cities is more diverse (or heterogeneous).

At a glance, it is difficult to discern which one of the two is more diverse.  So we need to compute the index of qualitative variation (IQV). To compute the (IQV) we apply the following formula. 

k(N² - sum(f²)) / N²(k - 1)

where:

k = number of categories

N = number of cases (total the frequency counts)

sum of f² = the sum of the squared frequencies (that is, square the frequencies first, then add them up)

The result should be something like this:

In the attached excel sheet, you will be able to audit the formula for IQV if you want excel to do your calculations.