Comparing the Arithmetic Mean, Geometric Mean, and Harmonic Mean
The arithmetic mean is what we usually call "average". You find the arithmetic mean by adding the numbers in a set of data and dividing by the number of pieces of data.
The harmonic mean of a set of numbers is defined as the reciprocal of the arithmetic mean of the reciprocals of the numbers. The harmonic mean for a and b can be computed using
If , then x is called the geometric mean between a and b.
Use a graphing program to investigate and compare these different measures of middle. What can you say about how the arithmetic mean compares to the geometric mean and the harmonic mean?
Submit your idea for an investigation to InterMath.
