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

 From: John Day Subject: Re: mean.m (a question of mathematics, not programming) Date: Wed, 21 Mar 2001 13:04:32 -0500

```Joshua,

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The arithmetic and geometric means both attempt to give an answer to the question "what is the _average_ value of a set of numbers?" An interesting property of both is that they return the same answer if the number are all the same: i.e. the average value of {5,5,5} (a.m. or g.m.) is 5. But the geometric mean is more 'sensitive' to values at or near zero, because the terms are multiplied rather than added. If the set contains a single zero, the g.m. will always be zero, it can never 'recover' by adding larger terms to offset the smaller terms, like you can do with the a.m.
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In fact, the g.m. is often employed when you want your estimate of the expected value to be very sensitive to the presence of values near or at zero.
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References? Any mathematical dictionary will do. I really like the Harper-Collins Dictionary of Mathematics. It's almost like a Master's Degree in a book.
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HTH,

John Day
Staff Scientist
Computer Science Innovations
http://www.csi.cc/~jday

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