Earth Mover's Distance Between Grade Distribution Data with Fixed Mean

Abstract

The Earth Mover's Distance (EMD) is examined on all theoretically possible grade distributions with the same grade point average (GPA). The numbers of distributions with the same EMD and GPA are encoded in the coefficients of a generating function. The theoretical mean EMD for grade distributions, that are sampled uniformly and independently at random, is computed from this function, and compared to real world grade data taken from several years. The data is further examined regarding the appearance of clusters that change when varying the distance threshold.