thesIt » standard deviation http://lakm.us/thesit computer science research log in semi microbloging style Tue, 24 Aug 2010 21:34:55 +0000 http://wordpress.org/?v=2.9 en hourly 1 Easiest description standard deviation http://lakm.us/thesit/288/easiest-standard-deviation-is-distance-f/ http://lakm.us/thesit/288/easiest-standard-deviation-is-distance-f/#comments Mon, 28 Jun 2010 22:27:38 +0000 Arif http://xp-racy.lan/s2/?p=287 Easiest description for standard deviation definition is distance from mean (expected value) as shown in this graphical depiction


where all the values fall at σ distance within the dotted circle radius. Of course a more real-life situation is shown as


where σ is the square root of the following mean
\sigma^2 =\frac{\sum_{i=1}^{n}{\sigma_{i}^2}}{n}

σ² a.k.a. variance is averaged quadratic distances. Explanation:

Distance may have several concepts, in this variance description, distance shows “how far” a value is from its population expected value (mean). Quadratic form of this “how far” is

\sigma_i=(x_i-\bar{x} )^2

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