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.
Loosely speaking, 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: [EMAIL PROTECTED]
<[EMAIL PROTECTED] 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.
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