Is there another name for power mean, where p=1/2

Question

What would you call this type of average?

$\left(\frac{1}{n} \sum_{i=1}^n \sqrt x_i \right) ^ 2$

I'd probably call it square-mean-root, but I don't know what the correct term would be. — Glen O, Apr 29 '13 at 01:10

score 1 · Answer 1 · answered Apr 29 '13 at 02:19

1

This is moderately special, but I don't think it is special enough to have its own name.

I would call it "1/2-power mean", with a possible explanation that the "$r$-power mean" of $(a_i)_{i=1}^n$ is $ (\frac1{n} \sum_{i=1}^n a_i^{r})^{1/r} $".

answered Apr 29 '13 at 02:19

marty cohen

107,799

score 1 · Accepted Answer · answered Apr 29 '13 at 02:19

1

Because it isn't used nearly as often as the arithmetic mean, geometric mean, or RMS, this mean doesn't have a common name other than just "the generalized mean with $p=1/2$".

answered Apr 29 '13 at 02:19

icurays1

17,161

Is there another name for power mean, where p=1/2

2 Answers2