We introduce from first principles an analysis of the information content of multivariate distributions as information sources. Specifically, we generalize a balance equation and a visualization device, the Entropy Triangle, for multivariate distributions and find notable differences with similar analyses done on joint distributions as models of information channels. As an example application, we extend a framework for the analysis of classifiers to also encompass the analysis of data sets. With such tools we analyze a handful of UCI machine learning task to start addressing the question of how well do datasets convey the information they are supposed to capture about the phenomena they stand for. (C) 2017 Elsevier Ltd. All rights reserved.