Why is the standard deviation [tex]\sigma =\sqrt{\frac{\sum_{i=1}^{n}\left( \overline{x}-x_{i}\right) ^{2}}{n-1}}[/tex] and not [tex]\sigma =\frac{\sum_{i=1}^{n}\left| \overline{x}-x_{i}\right| }{n}[/tex] or at least [tex]\sigma =\sqrt{\frac{\sum_{i=1}^{n}\left( \overline{x}-x_{i}\right) ^{2}}{n}}[/tex]?(adsbygoogle = window.adsbygoogle || []).push({});

I suppose that it has something to do with the normal distribution but I'm not sure in what way.

Thanks for the input.

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# Standard deviation

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