Cubic root of the mean of the cubes
The cubic mean (written as formula_1) is a specific instance of the generalized mean with formula_2. 
Definition.
For formula_3 real numbers formula_4 the cubic mean is defined as:
formula_5.
Applications.
The cubic mean is used to predict the life expectancy of machine parts.
The cubic mean wind speed has been used a measure of local potential for wind energy.
The cubic mean is also used in biology to measure the mean dimensions of spherical bacteria (cocci) and of larger animals that are approximately spheroidal in shape. 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.
References.
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