Comments on Nerdblog.com: the harmonic mean (MPG standards)

Oops: n=-1 is the harmonic mean. n=1 is the regula...

2008-01-22T02:32:00.000-08:00

Oops: n=-1 is the harmonic mean. n=1 is the regular arithmetic mean.

There's a beautiful inequality saying that if n is less than m then the nth power mean is less than the mth power mean.

For n=0 the definition doesn't make sense, but it can be shown that the nth power mean converges to the geometric mean (square root of X times Y) as n goes to 0.

This all can be generalized to arbitrarily many nonnegative quantities, with the same inequalities holding among their power means.

Way to go me, turning a topic of important social interest into abstract mathematical curiosa!

I just want to point out that the harmonic mean of...

2008-01-22T01:59:00.000-08:00

I just want to point out that the harmonic mean of X and Y is defined as 2/(1/X+1/Y), not 1/(1/X+1/Y). Fortunately, it looks like this was just a typo and you used the right formula in calculations.

More generally, the "n-th power mean" of two numbers X and Y is defined as ((X^n+Y^n)/2)^(1/n). n=1 corresponds to the Harmonic mean.

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