A Better Bound on the Variance

@article{Bhatia2000ABB,
  title={A Better Bound on the Variance},
  author={Rajendra Bhatia and Chandler Davis},
  journal={The American Mathematical Monthly},
  year={2000},
  volume={107},
  pages={353-357}
}
We will explain how it strengthens the existing bound. We will go on to show it as only a commutative special case of a far more general result; and then we will do the same for a new result analogous to it, in which the place of the square function is taken by the inverse function. To take the prototype situation first, let a1,... , a, be real numbers, assume M _ a1 and m _ a1 for all j, and set a for the average: a = 'L.a. 

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