Measuring variability and association for categorical data

The quantification of the variability of the categorical data is an important topic not only in statistics, but also in many other disciplines. We suggest different variability measures to describe the variability of categorical data. In our approach, any set of categorical data for a determinate categorical variable is treated as a fuzzy set. Therefore, measuring the variability of categorical data is the same as measuring its fuzziness. Different measures of association between two categorical variables are also proposed. The measures can be easily applied to categoric random variables.