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Upper and lower bounds are given for the difference between the arithmetic and geometric means of n positive real numbers in terms of the variance of these numbers.
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Cartwright et al. (Tue,) studied this question.
synapsesocial.com/papers/6a11c4ba276e1b6925c90c83 — DOI: https://doi.org/10.1090/s0002-9939-1978-0476971-2
D. I. Cartwright
M. J. Field
Imperial College London
Proceedings of the American Mathematical Society
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