Thecubic mean (written as${\displaystyle {\overline{x}}_{\mathrm{c}\mathrm{u}\mathrm{b}\mathrm{i}\mathrm{c}}}$) is a specific instance of thegeneralized mean with${\displaystyle p=3}$.

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

${\displaystyle {\overline{x}}_{\mathrm{c}\mathrm{u}\mathrm{b}\mathrm{i}\mathrm{c}}=\sqrt[3]{\frac{1}{n}\sum _{i=1}^n{x}_i^3}=\sqrt[3]{\frac{x_1^3+x_2^3+\cdots +x_n^3}{n}}.}$   ^[1][2][3]

For example, the cubic mean of two numbers is:

${\displaystyle \sqrt[3]{\frac{x_1^3+x_2^3}{2}}}$.

The cubic mean is used to predict thelife expectancy of machine parts.^[3][4][5][6]

The cubic mean wind speed has been used a measure of local potential forwind energy.^[7]

The cubic mean is also used inbiology to measure the mean dimensions of sphericalbacteria (cocci)^[8] and of larger animals that are approximately spheroidal in shape.^[9] In this case using the conventionalarithmetic mean will not give an accurate result because the size of a spherical bacterium increases as thecube of the radius.

• Means

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