This paper proposes an axiomatic foundation for new measures of polarization that can be applied to ordinal distributions such as self-assessed health (SAH) data. This is an improvement over the existing measures of polarization that can be used only for cardinal variables. The new measures of polarization avoid one difficulty that the related measures for evaluating health inequalities face. Indeed, inequality measures are mean based, and since only cardinal variables have a mean, SAH has to be cardinalized to compute a mean, which can then be used to calculate an inequality measure. In contrast, the new polarization measures are median based and hence do not require to impose cardinal scaling on the categories. After deriving the properties of these new polarization measures, we provide an empirical illustration using data from the British Household Panel Survey that demonstrates that SAH polarization is also a relevant question on empirical grounds, and that the polarization measures are adequate to evaluate polarization phenomena whereas inequality measures are not adequate in these cases.