# Skewness

The skewness of a data population is defined by the following formula, where μ_{2}
and μ_{3} are the second and third central moments.

Intuitively, the skewness is a measure of symmetry. As a rule, negative skewness indicates that the mean of the data values is less than the median, and the data distribution is left-skewed. Positive skewness would indicate that the mean of the data values is larger than the median, and the data distribution is right-skewed.

#### Problem

Find the skewness of eruption duration in the data set faithful.

#### Solution

We apply the function skewness from the e1071 package to compute the skewness coefficient of eruptions. As the package is not in the core R library, it has to be installed and loaded into the R workspace.

> duration = faithful$eruptions # eruption durations

> skewness(duration) # apply the skewness function

[1] -0.41355

#### Answer

The skewness of eruption duration is -0.41355. It indicates that the eruption duration distribution is skewed towards the left.

#### Exercise

Find the skewness of eruption waiting period in faithful.