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But representing skew is precisely to show how "off" from a Guassian it is.

Because real data is never perfectly Guassian, or perfectly anything.

But the idea of a box plot is that it's for data which is in theory Gaussian or a similar unimodal kind of bell-shaped curve.

Then you can look at the box plot and see if it actually is -- are the two boxes roughly equal-sized? Are the lines a bit longer than the boxes but not insanely so?



You model skew in Gaussian distributions by adding an exponential parameter.




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