In article <[EMAIL PROTECTED]>, [EMAIL PROTECTED] (Glen) wrote: >Subject: Re: a strange sort of average... name? >From: [EMAIL PROTECTED] (Glen) >Organization: http://groups.google.com >Date: 10 Mar 2004 17:52:52 -0800 >Newsgroups: sci.stat.edu > >[EMAIL PROTECTED] (Jason Owen) wrote in message >news:<[EMAIL PROTECTED]>... >> Hello, >> >> An engineering friend of mine has encountered this formula as >> a measure of "average" for a sample of N values: >> >> log (N) - log ( sum (10^-X) ) >> >> where X is a sample value and log is logarithm base 10. >> >> Has anyone encountered this before? The closest thing it >> resembles is the harmonic mean, but it's certainly not the >> same. > >It seems to combine the ideas of the harmonic mean >and another kind of mean that's like the anti-version >of the geometric mean. GM is exp of average logs, this >is - but in base 10 - like log of average exps, but >with the extra twist that the "average" in the middle >is the harmonic mean. Odd. > >What's the context? > >Glen
The data may be in an logarithmic scale (such as decibels of communications engineering) so what one has is a transformation back to a linear scale, an average on linear scaled dats and a transformation back to logarithmic scaling. The instruments may be reporting a level below a reference value so the minus sign accounts for the positive number reported for a fraction smaller than one. . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
