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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?


marked as duplicate by whuber Apr 5 '18 at 13:49

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  • $\begingroup$ 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. $\endgroup$ – Sideshow Bob Apr 5 '18 at 8:50
  • 1
    $\begingroup$ @SideshowBob well, all the means (arithmetic, geometric, harmonic, median, ...) are not dimensionless, either :) $\endgroup$ – bers Apr 5 '18 at 8:56
  • $\begingroup$ See this article? $\endgroup$ – Vincent Guillemot Apr 5 '18 at 9:38
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    $\begingroup$ This is called the Harmonic Mean. $\endgroup$ – whuber Apr 5 '18 at 13:49

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