  Data is one of the most important assets of the information age, and its
societal impact is undisputed. Yet, rigorous methods of assessing the quality
of data are lacking. In this paper, we propose a formal definition for the
quality of a given dataset. We assess a dataset's quality by a quantity we call
the expected diameter, which measures the expected disagreement between two
randomly chosen hypotheses that explain it, and has recently found applications
in active learning. We focus on Boolean hyperplanes, and utilize a collection
of Fourier analytic, algebraic, and probabilistic methods to come up with
theoretical guarantees and practical solutions for the computation of the
expected diameter. We also study the behaviour of the expected diameter on
algebraically structured datasets, conduct experiments that validate this
notion of quality, and demonstrate the feasibility of our techniques.
