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Date:

March 15, 2002 05:12Subject:

Re: Trouble with Math::NumberCruncher (fwd)Message ID:

Pine.OSF.4.10.10203151840060.477187-100000@brahma.igidr.ac.inHi Nick, I cannot tell you how ashamed I am. This should've been absolutely obvious to me (I also did graduate studies in Statistics, after which I switched to Economics, and Finance.) I guess it's TGIF feeling, or just workload, but my mind didn't perhaps work, when I failed to find this simple reason! Thanks very much, -tir On Fri, 15 Mar 2002 Nick_D_Montpetit@eFunds.com wrote: > > Hi Tirthankar, > > I knew my Graduate work in Statistics would come in handy at some point... > :-) Without looking at the documentation for Math:NumberCruncher, I can > fairly confidently say that both you and Math:NumberCruncher are right, but > you are trying to calculate different things. In the following > explanation, I'll use the statistical language loosely, because you'll want > to consult a statistics textbook (or possibly the documentation for > Math:NumberCruncher) for the details. > > If the numbers 0..20 represent a sample of 21 independent random variables > from a given population (or distribution), the estimated variance is indeed > 38.5. Keep in mind that this is an estimate of the true variance, which > presumably you don't know because you just have a sample of all possible > values. > > If the numbers 0..20 represent every possible value in the population, and > each value is equally likely, then the actual variance - which can be > calculated because you know each value and its probability - is 36.6666666, > and this is the value returned by Math:NumberCruncher. > > So one answer is an (unbiased) estimate of the true variance and the other > is a calculation of the true variance, and which one you use depends on > whether you have a sample or the entire population. In most cases (where > samples are involved) you'll want to use the first calculation. > > This relationship is true: (n-1)/n*(sample variance estimate) = (population > variance calculation) so that > > (20/21)* 38.5 = 36.66667 > > Hope this helps, > -Nick > > > > "Tirthankar > C. Patnaik" To: beginners@perl.org > <tir@igidr.ac cc: > .in> Subject: Trouble with Math::NumberCruncher > > 03/15/02 > 06:23 AM > > > > > > This might seem trivial, but it has me stumped. > > The variance of numbers 0..20 is 38.5. > Then why does Math:NumberCruncher show it as 36.6667? > > Here's a sample prog, and it's output. Here test04.dat is a file that has > numbers 0 to 20, on separate lines. > #-------------------start---------------- > #!/usr/bin/perl -w > use Math::NumberCruncher; > # Program to test Math::NumberCruncher > > # Get a file from STDIN, print the variance, and the std. deviation. > > @array = <>; > map {chomp} @array; > > $variance = Math::NumberCruncher::Variance(\@array); > $stddev = Math::NumberCruncher::StandardDeviation(\@array); > $sd2 = $stddev**2; > > print scalar(@array), "\n"; > > printf "Var=$variance, S.D=$stddev S.D^2 = $sd2\n"; > > exit; > #----------------end--------------------- > > And the output is: > > 21 > Var=36.6666666666667, S.D=6.05530070819498 S.D^2 = 36.6666666666667 > > > What could be possibly wrong? Even the standard value is wrong. > > > TIA, > -tir > > > -- > Tirthankar, IGIDR. > +91-22-8400919 x275 (r), x593(o), x542(CFL). > http://www.igidr.ac.in/~tir > > LEGACY, n. A gift from one who is legging it out of this vale of > tears. > > > -- > To unsubscribe, e-mail: beginners-unsubscribe@perl.org > For additional commands, e-mail: beginners-help@perl.org > > > > > > -- Tirthankar, IGIDR. +91-22-8400919 x275 (r), x593(o), x542(CFL). http://www.igidr.ac.in/~tir NON-COMBATANT, n. A dead Quaker.

**Re: Trouble with Math::NumberCruncher (fwd)**by Tirthankar C. Patnaik

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