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

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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Correspondence to Oscar Rojo.

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Rojo, O. Inequalities involving the mean and the standard deviation of nonnegative real numbers. J Inequal Appl 2006, 43465 (2006). https://doi.org/10.1155/JIA/2006/43465

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Keywords

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