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If the PDF the the variable is$$f(x)=\frac4\pi\fracx1+x^4\,

The average is therefore$$\frac4\pi\int_0^\infty\fracx^21+x^4\,\urbanbreathnyc.comrmdx=\sqrt2$$Yet the variance, for this reason the conventional deviation, is boundless since$$\frac4\pi\int_0^\infty\fracx(x-\sqrt2)^21+x^4\,\urbanbreathnyc.comrmdx$$diverges.

As with the distribution above, this indicates that the circulation is non-symmetric, a many the variance is added by the tail to the appropriate of the mean.

The sigma dominance only hold if the variable is generally distributed! In your case, the is probably since it all lies in the negative values? just imagine a high variance distribution and also then change to the left (take far a big value). Or it have the right to have fat tail. I suggest plot the data in some software program as a histogram, or density approximation and also it will be clear.

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Why the typical deviation approximated through the range rule of ignorance much different from the typical deviation calculated straight from sample data?

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