Cubic mean

The the average values associated cubic means of numerical values is defined as ${\displaystyle {\bar {x}}_{\mathrm {kubisch} }}$ ${\displaystyle n}$ ${\displaystyle x_{i}}$

${\displaystyle {\bar {x}}_{\mathrm {kubisch} }={\sqrt[{3}]{{\frac {1}{n}}\sum _{i=1}^{n}{x_{i}^{3}}}}={\sqrt[{3}]{{x_{1}^{3}+x_{2}^{3}+\cdots +x_{n}^{3}} \over n}}.}$

It is the basis for the definition of skewness in statistics.

It is also used in the service life prediction of machine parts in order to evaluate the load spectrum acting on the component in a key figure.

It can be described as generalized mean with conceive. ${\displaystyle p=3}$