Skewness

Skewness is a measure of the asymmetry of the distribution of a real-valued random variable. Roughly speaking, a distribution has positive skew if the asymmetry is towards the positive direction, and negative skew if it is towards the negative direction (i.e., positive skew if the positive tail is longer and negative skew if the negative tail is longer).

Skewness is defined as μ₃ / σ³, where μ₃ 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 / Nσ³, 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.