# Variation ratio

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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 percent of cases which are not the mode::$mathbf\left\{v\right\} := 1 - frac\left\{f_m\right\}\left\{N\right\}.$

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 in Harv|Freeman|1965.

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.

For example, a group which is 55% female has a variation ratio of 45% and is more dispersed in terms of gender than a group which is 95% female and has a variation ratio of only 5%. Similarly, a group which is 25% Catholic (where Catholic is the modal religious preference) has a variation ratio of 75% and is much more dispersed religiously than a group which is 85% Catholic and has a variation ratio of only 15%.

References

* Citation
last=Freeman
first=Linton C.
title=Elementary Applied Statistics
publisher=John Wiley and Sons
location=New York
year=1965
pages=40–43

ee also

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

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