When Averages Fail

The law of large numbers breaks

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

• Pareto mean: $\frac{\alpha}{\alpha - 1}$ times the minimum, infinite for $\alpha \le 1$.
• With heavy tails, running averages settle slowly or never.
• Use medians and concentration measures for heavy-tailed data.

Steps

1. Averages usually settle
2. Running averages
3. The true mean
4. Which summary?
5. Mean versus median
6. No mean at all