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

[John Day]

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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