88.27 More on spreads and non-arithmetic means

  title={88.27 More on spreads and non-arithmetic means},
  author={Douglas W. Mitchell},
  journal={The Mathematical Gazette},
  pages={142 - 144}
  • D. Mitchell
  • Published 1 March 2004
  • Mathematics
  • The Mathematical Gazette
88.27 More on spreads and non-arithmetic means Nick Lord [1] points out that (1) if all numbers in a set become proportionately farther from their fixed arithmetic mean (of course increasing their standard deviation), their geometric mean decreases, but (2) in general if the numbers are arbitrarily altered to increase their standard deviation, again with fixed arithmetic mean, their geometric mean may increase or decrease. 
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Does smaller spread always mean larger product?
  • N. Lord
  • Mathematics
    The Mathematical Gazette
  • 2002
86.34 Does smaller spread always mean larger product? For two positive real numbers with a given sum, it is easy to check that, the closer they are together, the greater is their product. In this