In probability theory and statistics,

**skewness**is a measure of the asymmetry of the probability distribution of a real-valued random variable. Roughly speaking, a distribution has positive skew if the if the positive tail is longer and negative skew if the negative tail is longer.

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 sample of *N* values the sample skewness is Σ_{i}(*x*_{i} − μ)^{3} / *N*σ^{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