Descriptive analysis of student ratings

Let X be a statistical variable representing student ratings of University teaching. It is natural to assume for X an ordinal scale consisting of k categories (in ascending order of satisfaction). At first glance, student ratings can be summarized by a location index (such as the mode or the median of X) associated with a convenient measure of ordinal dispersion. For instance, the median of X may be associated with the dispersion index of Leti, resulting in a synthesis that takes into account the ordinal nature of data and also communicates information in an effective way. More generally, there are many indexes (such as the ordinal entropy) that can be properly employed to measure the ordinal dispersion. On the other hand, student ratings are often converted into scores and treated as a quantitative variable. More generally, it is possible to measure student satisfaction by means of a real-valued function defined on the standard simplex and satisfying some appropriate conditions. Finally, such a measure of satisfaction can be associated with a suitable measure of variability.