How can a single introduction of our own [average], and that a fictitious one, possibly take the place of the many values which were actually given to us? And the answer surely is, that it can not possibly do so; the one thing cannot take the place of the other for purposes in general, but only for this or that specific purpose.

On the Nature and uses of Averages, Journal of the Royal Statistical Society, Volume 54, 1891 (p. 430)