- Research Article
- Open Access
Inequalities involving the mean and the standard deviation of nonnegative real numbers
- Oscar Rojo1Email author
https://doi.org/10.1155/JIA/2006/43465
© Oscar Rojo. 2006
- 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
.
Keywords
- Standard Deviation
- Positive Integer
- Real Number
- Large Component
- Nonnegative Real Number
Authors’ Affiliations
References
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Copyright
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.
