Standardafvigelse

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Standardafvigelsen eller spredningen bruges inden for statistik og er et udtryk for, hvordan en række målinger eller observationer fordeler sig omkring disses gennemsnit. Standardafvigelsen, σ, er defineret som:

$\sigma = \sqrt{\frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2}$ .

Hvor x_i for i = 1..N er observationerne og $\overline{x}$ er gennemsnittet af disse værdier.

Standardafvigelsen er altså kvadratroden af gennemsnittet af kvadraterne på den enkelte observations afvigelse fra gennemsnittet. Det betyder, at én stor afvigelse har større indflydelse end mange små. Således vil 1 observation med afvigelse på 2 bidrage med en størrelsesorden af 4, hvor 2 observationer med en afvigelse på 1 samlet kun vil bidrage med en størrelsesorden af 2. Dette betyder igen, at blot en enkelt fejlobservation kan påvirke standardafvigelsen meget – hvor det vil påvirke gennemsnittet i mindre grad.

Begrebet standardafvigelse kan defineres på en analog vis for de fleste sandsynlighedsfordelinger.

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STATIC WIKIPEDIA JUNE 2008 on wikipedia2006.classicistranieri.com

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STATIC WIKIPEDIA MARCH 2008 on wikipeda2006classicistranieri.com
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STATIC WIKIPEDIA APRIL 2007 on wikipeda2006classicistranieri.com
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STATIC WIKIPEDIA DECEMBER 2006 on wikipeda2006classicistranieri.com
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STATIC WIKIPEDIA NOVEMBER 2006 on wikipeda2006classicistranieri.com
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