A refinement of the arithmetic mean-geometric mean inequality

D. I. Cartwright, M. J. Field
1978 Proceedings of the American Mathematical Society  
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.
doi:10.1090/s0002-9939-1978-0476971-2 fatcat:zh3zemgagfhjld4uqyssjh54ou