Why do Excel and WolframAlpha give different values for skewness

for the following 3 values 222,1122,45444

WolframAlpha gives 0.706

Excel, using =SKEW(222,1122,45444) gives 1.729

What explains the difference?

Answer

They are using different methods to compute the skew. Searching in the help pages for skewness() within the R package e1071 yields:

Joanes and Gill (1998) discuss three methods for estimating skewness:

Type 1:
g_1 = m_3 / m_2^(3/2). This is the typical definition used in many older textbooks.
Type 2:
G_1 = g_1 * sqrt(n(n-1)) / (n-2). Used in SAS and SPSS.
Type 3:
b_1 = m_3 / s^3 = g_1 ((n-1)/n)^(3/2). Used in MINITAB and BMDP.
All three skewness measures are unbiased under normality.

#Why are these numbers different?
> skewness(c(222,1122,45444), type = 2)
[1] 1.729690
> skewness(c(222,1122,45444), type = 1)
[1] 0.7061429

Here’s a link to the paper referenced if someone has the credentials to get it for further discussion or education: http://onlinelibrary.wiley.com/doi/10.1111/1467-9884.00122/abstract

Attribution
Source : Link , Question Author : Scott Weinstein , Answer Author : Chase

Leave a Comment