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.png

 

 

Sample Skew (

image\samskew.png

  

 

(adapted from King and Julstrom, 1982 and Hildebrand, 1986)

 

where

= Population Standard Deviation

s

= Sample Standard Deviation

= Population Mean

= 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