Subtracting_N-1

# Subtracting_N-1 - Variances N vs N-1(1995 Seal.< file...

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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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## This note was uploaded on 10/08/2010 for the course STAT 500 at Penn State.

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Subtracting_N-1 - Variances N vs N-1(1995 Seal.< file...

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