Variation ratio

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:

$𝐯:=1-\frac{f_m}{N},$

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 Template:Harv.

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

$𝐯:=1-\frac{0.55}{1}=0.45,$

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 is

$𝐯:=1-\frac{60}{100}=0.4,$

See also

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

References

• Template:Citation