Skewness

Overview

Probability theory

Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...

and statistics

Statistics

Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

,

**skewness**is a measure of the asymmetry of the probability distribution

Probability distribution

In probability theory, a probability mass, probability density, or probability distribution is a function that describes the probability of a random variable taking certain values....

of a real

Real number

In mathematics, a real number is a value that represents a quantity along a continuum, such as -5 , 4/3 , 8.6 , √2 and π...

-valued random variable

Random variable

In probability and statistics, a random variable or stochastic variable is, roughly speaking, a variable whose value results from a measurement on some type of random process. Formally, it is a function from a probability space, typically to the real numbers, which is measurable functionmeasurable...

. The skewness value can be positive or negative, or even undefined. Qualitatively, a negative skew indicates that the

*tail*on the left side of the probability density function is

*longer*than the right side and the bulk of the values (possibly including the median) lie to the right of the mean. A positive skew indicates that the

*tail*on the right side is

*longer*than the left side and the bulk of the values lie to the left of the mean.

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