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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.