ASM page 309 #22.2

[actuary_pilot]

On the following problem, the book divides each of the values by 100, and gets an answer of 1.291. I worked the problem as it was given, and got 12.91 - off by a factor of 10. I cannot find a mistake in my arithmatic. Can anyone see the mistake I made, or is there a flaw in stating as the book states (the coefficient of skewness is scale free, so lets divide all observations by 100). Either I or the book is off by a scale of ten - the square root of 100.

A sample has the following observations:

2 observations of 400
7 observations of 800
1 observation of 1600

Calculate the coefficient of skewness:

E(x) = (2*400+7*800+1600)/10 = 800
Var(X) = (2*(-400)^2+800^2)/10=96,000
SD(X)=96,000^.5=309.84
E((X-E(X))^3) = (2*(-400)^3+800^3)/10 = 384,000,000

Skewness = 384,000,000/309.84^3=12.91

[Gandalf]

E((X-E(X))^3) = (2*(-400)^3+800^3)/10 = 384,000,000
Excel disagrees with your result of that calculation.

[BigDawg]

I agree with your calculations, except for the second last last line of your solution.

(2*(-400)^3+800^3)/10 = 38,400,000

I think you forgot to divide by ten.

[actuary_pilot]

Thank you. I guess I am studying too hard and am starting to see extra zeros. I re-worked on my calculator again, and didn't see the extra zero this time.