What is "skewness"

1877, from skew + -ness.

n. 1 The property of being skew. 2 (context statistics English) A measure of the asymmetry of the probability distribution of a real-valued random variable; is the third standardized moment, defined as $scriptstylegamma\_1\; =\; frac\{mu\_3\}\{sigma^3\},\; !$ where $mu\_3$ is the third moment about the mean and $sigma$ is the standard deviation.

n. an oblique or slanting asymmetry [syn: lopsidedness]

In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive or negative, or even undefined.

The qualitative interpretation of the skew is complicated. For a unimodal distribution, negative skew indicates that the tail on the left side of the probability density function is longer or fatter than the right side – it does not distinguish these shapes. Conversely, positive skew indicates that the tail on the right side is longer or fatter than the left side. In cases where one tail is long but the other tail is fat, skewness does not obey a simple rule. For example, a zero value indicates that the tails on both sides of the mean balance out, which is the case for a symmetric distribution, but is also true for an asymmetric distribution where the asymmetries even out, such as one tail being long but thin, and the other being short but fat. Further, in multimodal distributions and discrete distributions, skewness is also difficult to interpret. Importantly, the skewness does not determine the relationship of mean and median.