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: 8 November 2006

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 .

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Authors’ Affiliations

(1)
Departamento de Matemáticas, Universidad Católica del Norte

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Copyright

© Oscar Rojo. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.