Correlation coefficients, coefficients of variations, standard deviations, slopes, tangents, cosines, densities, temperatures, dissimilar ratios, and intensive properties in general are not additive. Therefore, arithmetic averages cannot be computed out of any of these.
Still, from time to time some “experts” and pseudo “scientists” do that.
Want to know why this is not mathematically and statistically possible? This is the subject of a paper I wrote and that is about to be published in Communications in Statistics – Theory and Methods (by Taylor & Francis).
Incidentally, I will provide a preview of the topic to the search marketing community. Thanks to my dear friend, Mike Grehan, this will be the topic I’ll be speaking about at the March, 2012 SES, NY.