Chebyshev's inequality says: P(|X-μ| ≥ kσ) ≤ 1/k²

Ever wonder how likely it is to deviate from the average?

Imagine you're at a carnival, and there's a game where you roll a die. The prize is awarded if you roll a number more than 2 standard deviations away from the average roll.

Chebyshev's inequality tells us that even without knowing the exact distribution of the rolls, we can say there's a certain chance of winning the prize if we roll a number that's unusually high or low compared to the average.

Example

If the average roll is 3.5 and the standard deviation is 1, rolling a 7 or lower is an unusual outcome.

Remember this

Chebyshev's inequality helps us understand the likelihood of rare events happening in random situations.

Text adapted from Wikipedia, licensed under CC BY-SA 4.0.

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