Should we report a ratio of averages (RA) or an average of ratios (AR)? The answer depends on what we want to average and how. By definition, things that are not additive cannot be averaged in the arithmetic sense. This includes things like standard deviations, correlation coefficients, slopes, tangents, sines, cosines,… In the case of properties of matter, these can be classified as extensive or intensive. Extensive properties can be added together and averaged. By contrast, intensive properties are not additive so they cannot be averaged. The ratio of two intensive or two extensive properties is classified as an intensive ratio. These ratios are not additive either. For instance mass, volume, and moles are extensive properties so density (mass/volume) and molar concentrations (moles/volume) are intensive ratios. Do not average them in the arithmetic sense.…