Coefficient of skewness formula - Assignment Y1 - Question Y1.2 ii b

[stressed_and_depressed]

I don't understand how the solutions derive the skewness term (numerator) in the coefficient of skewness. Can someone please explain?

I get that : skew = E((X-mu)^3)

but where does the length term in the solutions come from?!

solutions: skew <- sum((x-mean(x))^3)/length(x)

Thanks!!

 

[John Lee]

You're confusing the model/population skewness of a distribution with the sample skewness.

The formula for the sample skewness is \(1/n \sum (x-\bar{x})^3\)

 

[stressed_and_depressed]

Would've taken me a million years to figure that out - thank you very much!