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  • Research Article
  • Open Access

Inequalities involving the mean and the standard deviation of nonnegative real numbers

Journal of Inequalities and Applications20062006:43465

https://doi.org/10.1155/JIA/2006/43465

  • Received: 22 December 2005
  • Accepted: 21 September 2006
  • Published:

Abstract

Let and be the mean and the standard deviation of the components of the vector , where with a positive integer. Here, we prove that if , then for . The equality holds if and only if the largest components of are equal. It follows that is a strictly increasing sequence converging to , the largest component of , except if the largest components of are equal. In this case, for all .

Keywords

  • Standard Deviation
  • Positive Integer
  • Real Number
  • Large Component
  • Nonnegative Real Number

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Authors’ Affiliations

(1)
Departamento de Matemáticas, Universidad Católica del Norte, Antofagasta, Casilla, 1280, Chile

References

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