The cubic mean (written as 
For 
![{\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}}.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b779561c8e64a5bfda052e9a4847cb7683e25b7c)
[1][2][3]For example, the cubic mean of two numbers is:
![{\displaystyle {\sqrt[{3}]{\frac {x_{1}^{3}+x_{2}^{3}}{2}}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e600e24ebb4cc85ef2dc73bafdab5366ff343693)
.The cubic mean is used to predict the life expectancy of machine parts.[3][4][5][6]
The cubic mean wind speed has been used a measure of local potential for wind energy.[7]
The cubic mean is also used in biology to measure the mean dimensions of spherical bacteria (cocci)[8] and of larger animals that are approximately spheroidal in shape.[9] In this case using the conventional arithmetic mean will not give an accurate result because the size of a spherical bacterium increases as the cube of the radius.
