Skewness, the third standardized moment, is defined as μ_{3} / σ^{3}, where μ_{3} is the third moment about the mean and σ is the standard deviation. The skewness of a random variable X is sometimes denoted Skew[X].
For a set of N values the skewness can be calculated as Σ_{i}(x_{i}  μ)^{3} / Nσ^{3}, where x_{i} is the i^{th} value and μ is the mean.
If Y is the sum of n independent random variables, all with the same distribution as X, then it can be shown that Skew[Y] = Skew[X] / √n.
Given samples from a population, the equation for population skewness above is a biased estimator of the population skewness. An unbiased estimator of skewness is
where σ is the sample standard deviation and μ is the sample mean.
See also: mean, variance, kurtosis.
Search Encyclopedia

Featured Article
