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Arif

  • 10:27:38 pm on June 28, 2010 | # | 0
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    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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