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## Re: mean.m (a question of mathematics, not programming)

 From: Benjamin Bunck Subject: Re: mean.m (a question of mathematics, not programming) Date: Wed, 21 Mar 2001 11:50:16 -0600 (CST)

```The geometric mean, like all means, is mostly useful to get an idea of the
"average" behavior of a group of numbers under some particular
mathematical operation. For instance, the additive (usual) mean of a group
of n numbers gives you  the unique number such that if all elements were
replaced by the avg, the sum would be the same.  The geometric mean of a
group of n numbers gives you a number such that if each member of the
group were replaced by the geometric mean, the product of the elements
would remain the same.

One application of the geometric mean (which, for x in R(n x 1) is
defined as the nth root of the product of the n elements) can be used for
gaining insight into interest rates.  For instance, if I have an account
that pays 15%,12%, and 8% in each of 3 consecutive years, I can find the
"average" interest
rate by the geometric mean, not the additive mean, of 1.15,1.12, and 1.08.
The will give me the exact single rate that would give me an identical
return (assuming annual compounding) to my original investment over 3
years.

hope this helps

Ben

On Wed, 21 Mar 2001, Joshua Rigler wrote:

> Risking ridcule by numericists and mathematicians alike, I bravely put
> forth what may very well be a dumb (and perhaps inappropriate for this
> mailing list) question...
>
> Would somebody be willing to tell me what the "geometric" and "harmonic"
> options are in the mean.m function?  Actually, I can see "what" they are
> in the source code, but I'd like to know what practical significance
> they might have.  References would be greatly appreciated.
>
> -EJR
>
>
>
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