# Comparing the Arithmetic Mean, Geometry 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?