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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


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.

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.

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.


John Day
Staff Scientist
Computer Science Innovations

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