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 ()

Sample Skew ()

(adapted from King and Julstrom, 1982)

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