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From: Alexandre Eremenko (no email)
Date: Wed Apr 20 2005 - 17:41:29 EDT
Dear George,
1. For OUR purposes, division by 6 and division by 7
are of course indistinguishable (sqrt{7/6}=1.08).
2. But in general, there are two kinds of standard deviation.
a) Population "standard deviation",
sqrt(sum (x_j-x)^2/n) (where x is the average and n the number
of observations),
and the
b) Sample standard deviation, similar formula but with n-1
instead of n.
In the problem of our type, when you want to
estimate the unknown standard deviation of
some "population" (sorry, this is a technical term),
from a finite sample
of this
population, the right thing to use is the Sample
standard deviation. (The difference between the two is non-negligible
only for small samples).
(My calculator actually has two separate buttons for these
two kinds of standard deviation).
The technical explanation of advantages of the
"sample SD" in comparison with "population SD"
is something I don't want to go into on this list.
(Stated very briefly, and in technical language it
is because the sample SD in an UNBIASED estimate for
the actual SD, while population SD is BIASED).
For details (which, I repeat, are IRRELEVANT for
a practical navigator), see any good course of
statistics) or type these words "sample standard deviation"
and "population standard deviation" on the web.
For example, http://www.quickmba.com/stats/standard-deviation/
Besides, sample SD is larger than population SD,
and I always want to be on the same side:-)
On an earlier remark of Fred Hebbard
(Tue Apr 19 2005 - 22:46:11 EDT )
"I would prefer that the standard deviations
be given to an extra digit".
my question is "What for?" I mean what can be a possible
use of this extra digit be?
Alex.
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