The variation ratio is a simple measure of statistical dispersion in nominal distributions; it is the simplest measure of qualitative variation.
It is defined as the proportion of cases which are not in the mode category:
where fm is the frequency (number of cases) of the mode, and N is the total number of cases. While a simple measure, it is notable in that some texts and guides suggest or imply that the dispersion of nominal measurements cannot be ascertained. It is defined for instance by .
Just as with the range or standard deviation, the larger the variation ratio, the more differentiated or dispersed the data are; and the smaller the variation ratio, the more concentrated and similar the data are.
An example
A group which is 55% female and 45% male has a proportion of 0.55 females (the mode is 0.55), therefore its variation ratio is
Similarly, in a group of 100 people where 60 people like beer 25 people like wine and the rest (15) prefer cocktails, the variation ratio is
See also
Qualitative variation, for a number of other measures of dispersion in nominal variables