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I have data that I plotted with a normal distribution and a QQ plot. I was wondering especially in QQ plot it seems that 95.4% of the data is normally distributed.

My question is what does numbers meanings that above 2 sigmas in QQ plot? Should remove them or I need to transform this variable and make it more normally distributed?

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The normal distribution is a theoretical model of data. Empirical data can be distributed more similarily or more dissimilarly to a normal distribution.

That empirical data has a couple of notable divergences from a theoretical normal distribution:

  • Presence of outliers
  • Not symmetric
  • Relative "peakedness"

Depending on your goal, you can pick a better model or transform the data to fit the normal distribution model. The power-law distribution might be a better model for the data. If you want to transform the data to better fit to a normal distribution, you can drop the outliers and then apply a log transformation.

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  • $\begingroup$ Thanks that's an excellent explanation. $\endgroup$ – Alexander Aug 31 '19 at 17:55

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