© 2019 Informa UK Limited, trading as Taylor & Francis Group. A family of variation measures for ordinal data or ordinal time series is considered. The asymptotic distribution of these measures is derived under different scenarios, and the performance of the resulting approximations is investigated with simulations. Possible applications include the bias correction of point estimates, the computation of confidence intervals as well as a test for maximal dispersion. A couple of real-data examples are presented to illustrate the application and interpretation of the ordinal variation measures.