Cubic mean

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

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

It is used for predicting the life expectancy of machine parts.[2][3]

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