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Topic: Squares intead Module in standard deviation
Replies: 3   Last Post: Oct 14, 2013 6:54 PM

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Virgil

Posts: 8,833
Registered: 1/6/11
Re: Squares intead Module in standard deviation
Posted: Oct 12, 2013 3:15 AM
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In article <X9-dnYiwhco8c8XPnZ2dnUVZ_oWdnZ2d@giganews.com>,
fom <fomJUNK@nyms.net> wrote:

> On 10/11/2013 11:56 PM, Christiano wrote:
> > Why in the formula of standard deviation uses squares instead of simply
> > putting differences within module?
> >
> > Example:
> > standard deviation² = Sum[(y-ym)²]/(n-1)
> >
> > Is not it better this?
> > standard deviation = Sum[|y-ym|]/(n-1)


This one, or rather Sum[|y-ym|]/n, is more commonly called the
mean absolute deviation rather than standard deviation.

http://pic.dhe.ibm.com/infocenter/spssas/v1r0m0/index.jsp?topic=%2Fcom.ib
m.spss.analyticcatalyst.help%2Fanalytic_catalyst%2Fmeanmedianabsolutedevi
ation.html
> >
>
> Your answer is probably here:
>
> http://en.wikipedia.org/wiki/Standard_deviation#Relationship_between_standard_
> deviation_and_mean
>
> The standard deviation satisfies a minimization problem with
> respect to the mean.
>
> As a general criterion for dispersions to points of central
> tendency, there is a small table here:
>
> http://en.wikipedia.org/wiki/Central_tendency#Solutions_to_variational_problem
> s
>
> Click on the other dispersions to find if any of the others
> relates to your "better" choice.

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