Consider two rates, $0 < x, y < 1$. How would one call $z$, if
$z = \frac{x*y}{(x+y)/2} = \frac{2*x*y}{x+y}$?
Is there a relationship with other means, such as the Inequality of arithmetic and geometric means?
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That quantity would be more likely to have a name if it were dimensionless i.e. if you took the square root of the numerator. Still not sure if it does, though. – Sideshow Bob Apr 05 '18 at 08:50
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1@SideshowBob well, all the means (arithmetic, geometric, harmonic, median, ...) are not dimensionless, either :) – bers Apr 05 '18 at 08:56
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See [this article](https://www.jstor.org/stable/2285338?seq=1#page_scan_tab_contents)? – Vincent Guillemot Apr 05 '18 at 09:38
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1This is called the *Harmonic Mean.* – whuber Apr 05 '18 at 13:49