I met the following equation.
$b=\frac{\sum_{i=1}^{N}x_i^2 }{\sum_{i=1}^{N}x_i }$, $0<x_i<1$
$x_i$ are probabilities.
Is it a kind of mean value? It seems that it is used as a mean value related to the fluctuation degree of a series of data. Is it right?
If so, in what case should it be used? And what is the difference between it and arithmetic mean or geometric mean?
if not, what does the equation mean?
update
In wiki I found that the equation above is contra-harmonic mean.
(link: https://en.wikipedia.org/wiki/Contraharmonic_mean )
I'm still wondering in what case should contra-harmonic mean be used. For example, when calculating the average of growth rates, geometric mean should be choosen. But what about contraharmonic mean?