median
don steward
mathematics teaching 10 ~ 16

Saturday 5 November 2011

some means

the arithmetic mean of two numbers is












and the geometric mean of two numbers is
 








find the arithmetical mean and geometrical mean for:

a = 2, b = 18
a = 3, b = 27
a = 1, b = 81
a = 4, b = 16
a = 2, b = 50
a = 5, b = 20

  • when is the arithmetical mean closest to the geometric mean?
  • how close can they be?
  • which one is larger?
  • does this happen for larger sets of numbers?
  • for just two numbers: prove, by squaring, that the arithmetical mean is larger than or equal to the geometric mean

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