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Is there a mathematical term for the ratio of arithmetic mean to the root mean square average?

(FWIW, in the context where I'm concerned about this the component values will always be >= 0.)

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The nearest thing I can think of (but it is not quite there!) is the signal to noise ratio. The reciprocal is called the Coefficient of Variation, and a few other names. The article has a link to SNR.

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It's not quite the coefficient of variation, but there's an algebraic relation along the lines of $\sqrt{1-(\frac\sigma\mu)^2}$ (though the signs in that expression come out differently each time I try to derive it, so caveat lector!) –  Henning Makholm Aug 22 '12 at 16:40
    
To be more accurate, the quantity that OP is interested in is equal to $1/\sqrt{\text{COV}^2+1}$, or $\cos(\arctan( \text{COV}))$ –  Erick Wong Aug 22 '12 at 16:41
    
CV appears to relate mean to standard deviation, and I'm taking the ratio of mean and RMS average, which is not quite the same thing. –  Daniel R Hicks Aug 22 '12 at 17:21
    
+1 as the question immediately made me think of BEE in Navy ET school during the communications phase. Sorry, nothing more or better to contribute. –  Chris K Oct 29 '13 at 0:34
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