The Empirical Rule & Chebyshev’s Theorem

The Empirical Rule

The Empirical Rule is just a really basic rule of thumb for estimating the width of a bell curve based on standard deviation, or estimating standard deviation based on a bell curve (divide the width of the bell by 4).

Chebyshev’s Theorem

This is basically just like the Empirical Rule except that it works for any distribution, not just bell-shaped normal-ish distributions. It even works for bimodal distributions, though it's so vague that it barely matters.