We present a variant of the Taylor diagram, a type of two-dimensional plot that succinctly shows the relationship between two or more random variables based on their variance and correlation. The Taylor diagram has been adopted by the climate and geophysics communities to produce insightful visualizations, e.g., for intercomparison studies. Our variant, which we call the "mutual information diagram," represents the relationship between random variables in terms of their entropy and mutual information, and naturally maps well-known statistical quantities to their information-theoretic counterparts. Our new diagram is able to describe nonlinear relationships where linear correlation may fail; it allows for categorical and multivariate data to be compared; and it incorporates the notion of uncertainty, key in the study of large ensembles of data.