Coefficient of Skewness

Skew is a measure of asymmetry in the distribution. A positive skew indicates a longer tail to the right, while a negative skew indicates a longer tail to the left. A perfectly symmetric distribution, like the normal distribution, has a skew equal to 0. For small data sets this measure is unreliable.

Population Skew ( $image\popskew-y1.gif$ )

$image\popskew.gif$

Sample Skew ( $image\samskew-g1.gif$ )

$image\samskew.gif$

$image\skew.gif$

(adapted from King and Julstrom, 1982)

where

$image\popsd-sym.gif$	= Population Standard Deviation
S	= Sample Standard Deviation
$image\u.gif$	= Population Mean
$image\mean.gif$	= Sample Mean
N	= number of data values for a population
n	= number of data values for a sample
xi	= ith data value