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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,

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