The cubic mean (written as ${\bar {x))_{\mathrm {cubic} )$ ) is a specific instance of the generalized mean with $p=3$ .

## Definition

For $n$ real numbers $x_{i}\in \mathbb {R}$ the cubic mean is defined as:

${\bar {x))_{\mathrm {cubic} }={\sqrt[{3}]((\frac {1}{n))\sum _{i=1}^{n}{x_{i}^{3))))={\sqrt[{3}]((x_{1}^{3}+x_{2}^{3}+\cdots +x_{n}^{3)) \over n)).$ For example, the cubic mean of two numbers is:

${\sqrt[{3}]{\frac {x_{1}^{3}+x_{2}^{3)){2)))$ .

## Applications

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

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