So I’ve got to take a sample of graphs and diddle around with the density (i.e. density of the graph) distribution of the sample. One field that I need to give is skew. I’ve searched the web, I’ve checked about 10 stats books, and all I can find is a quality, i.e. left-skewed or right-skewed. I need to quantify it.
Has anyone heard of a quantity called skew or skewedness?
Not off the top of my head. But the difference between the mean and the median should give you a rough idea of how skewed the data is, and the sign will tell you in which direction.
On a hunch, I went looking in the Excel help files. There is a function, SKEW, which returns the skewness of a dataset:
The formula is n/((n - 1)(n - 2) * sum(((x - x[sub]j[/sub])/s)^3, 0 < j < n - 1), where s is the sample standard deviation and x is the sample mean.
Maybe this will help?
Gah! I even searched for “skew” and “skewedness” on MathWorld. Thanks a lot guys! That should do it!
I believe the measure is called “kurtosis.”
Well, kurtosis measures peakedness (sort of the vertical skewness), but not what you are asking for. My textbook says skewness is measures by “Sk” where:
Sk = 3 x (sample mean-sample median) / sample standard deviation
The value of Sk ranges from -3 to 3, where perfectly symmetric is 0. If Sk is positive it is skewed right.