Cubic mean

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The cubic mean (written as ) is a specific instance of the generalized mean with .


For real numbers the cubic mean is defined as:


For example, the cubic mean of two numbers is:



It is used for predicting 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.


  1. ^ "calculation formulas" (PDF).
  2. ^ Svarovski, Ladislav (31 October 2000). Solid-Liquid Separation. ISBN 9780080541440. Retrieved 2015-01-20.
  3. ^ a b "Equivalent Load". Creative Motion Control. Archived from the original on 2015-01-20. Retrieved 2015-01-19.
  4. ^ "ISO 4301-1-1986 Cranes and lifting appliances; Classification; Part 1 : General". 1986. also available from "". Retrieved 2015-01-20.
  5. ^ Babu & Sridhar (2010). Design of Machine Elements. ISBN 9780070672840. Retrieved 2015-01-20.
  6. ^ Harris, Tedric A.; Kotzalas, Michael N. (9 October 2006). Essential Concepts of Bearing Technology, Fifth Edition. ISBN 9781420006599. Retrieved 2015-01-20.
  7. ^ Da Rosa, Aldo Vieira (2013). Fundamentals of renewable energy processes. p. 696. ISBN 9780123972194.
  8. ^ Rodina, Antonina Gavrilovna (1972). Methods in aquatic microbiology. p. 158. ISBN 083910071X.
  9. ^ Rice, Dale W.; Wolman, Allen A. (1971). The life history and ecology of the gray whale (Eschrichtius robustus). Stillwater, Oklahoma: American Society of Mammalogists. p. 34.