Scewness and Kurtosis

[olsick5]

Could someone please explain/compare/contrast these two concepts? I took the time to do the math on them over the last two hours and now feel like jumping out of a building. Thanks!

 

[Chuckrox8]

Skewness is how disproportionate the distribution is around the mean. Basically, it measures the shift away from a normal distribution. It’s measures how lopsided your graph is whether it’s to the left or right. If your mean=median=mode your distribution and chart would look perfectly normal. A normal chart would also exhibit kurtosis of 3, which is normal and simply measures the “peakness” of the distribution. You won’t have to calculate kurtosis on the exam.

 

[A Beaverhausen]

Variance, skewness and kurtosis are all central moments about the mean of a distribution. Variance is the second central moment; skewness the third and kurtosis the fourth. This curriculum might skip over the concept of a “moment” (I’m not sure because I don’t have the CFA texts yet), but I find that it’s first helpful to know what a concept is before we jump right to the graphs.
So in the end, you will learn about skewness and kurtosis in relation to symmetry and flatness – the graphic concepts. But if you start with the idea of central moments and variance, and then realize that the exponents are increasing (skewness, n = 3, kurtosis = 4), your brain might understand better.

 

[olsick5]

My brain understands the concepts a lot better thanks to the help of both of you. I appreciate it.