Coefficient of Skewness

The coefficient of skewness 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 zero. For small data sets this measure is unreliable.

Population Skew (image\popskew-y1.png

image\popskew.png

Sample Skew (image\samskew-g1.png

image\samskew.png

(adapted from King and Julstrom, 1982)

where

image\popsd-sym.png

= Population Standard Deviation

S

= Sample Standard Deviation

image\u.png

= Population Mean

image\mean.png

= Sample Mean

N

= number of data values for a population

n

= number of data values for a sample

xi

= ith data value

See Also

Data Statistics

95% and 99% Confidence Interval for the Mean

Average Deviation

Coefficient of Kurtosis

Coefficient of Variation

Critical Value of K-S Statistic at 90%, 95%, and 99% Significance Level

Kolmogorov-Smirnov Goodness of Fit Statistic for Normal Distribution

Mean

Standard Deviation

Standard Error of the Mean

Statistics References

Variance