A Family of Means

Harmonic, geometric, arithmetic

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Average speeds over equal distances use the harmonic mean.
• Harmonic ≤ geometric ≤ arithmetic ≤ quadratic mean.
• AM–GM extends to any number of terms.

Steps

1. Average speed
2. Four means
3. The chain of means
4. The harmonic mean
5. Geometric mean
6. Three numbers