Talk:Statistics/Summary/Averages/Geometric Mean

The presentation in the linked page is unsatisfying in the extreme. While it is true that the calculation of the arithemetic mean is more complicated for fractions, this does not mean that the arithmetic mean is a poor representation of the central tendency, as the text claims. In fact, the arithmetic mean is the arithemetic mean, and is a perfectly valid expression of the central tendency of fractions. The geometric mean is another measure of central tendency. Compare with the harmonic mean, for which an example is provided of why the arithemetic mean is not great, or at least an example where the harmonic mean has an appealing interpretation.

Can an example be provided showing when one would prefer the geometric mean to the arithmetic mean, including an interpretation?