Cubic mean

The cubic mean ${\bar {x}}_{\mathrm {cubic} }$ of $n$ real numbers $x_{i}\in \mathbb {R}$ is defined as:

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

It is used for predicting the life expectancy of machine parts.

It can be understood as the generalized mean with $p=3$.