Variation ratio explained

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:

v : = 1 - (f _{m})/(N) ,

where f_m 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

v : = 1 - (0 . 55)/(1) =0 . 45 , 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 isv : = 1 - (60)/(100) =0 . 4 ,

See also

• Qualitative variation, for a number of other measures of dispersion in nominal variables