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Variances, N vs N-1 (1995) Seal.<- file 95varqn.html ->
... divide by N or N-1 for variance? Seal
=====================David Seal, 06 Nov 1995========ssm, .
..
From: [email protected] (David Seal)
Newsgroups: sci.math.num-analysis,sci.math,sci.stat.math
Subject: Re: What's Standard Deviation?
Message-ID: <[email protected]>
[email protected] (Zhang Hongyu) writes:
>Can u tell me which definition is correct for Standard Deviation,
>
----------
----------
>
/ (X-EX)2
/ (X-EX)2
>
/-----------
or
/-----------
?
>
V
N
V
N-1
>
>where
>
EX means the Expectation(average value) of X. X2 means square of X.
>
>I've met both of these definitions in several cases, so I wonder
>what's their difference?
They're both valid (apart from some typos), but in different
circumstances. Basically, the first is a formula in probability (where
you're dealing with a known distribution); the second is one in
statistics (where you're dealing with an unknown distribution).
In probability, given a known distribution for X, the variance is
E((X-E(X))^2). If there are a finite number N of equiprobable values
for X, this is the same as:
SUM((X-E(X))^2)
---------------
N
The standard deviation is the square root of this variance, giving a

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