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

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

Chebyshev's inequality provides an upper bound on the probability of deviation from the mean for any random variable with finite variance.

Example

If a random variable X has a mean μ of 50 and a standard deviation σ of 10, Chebyshev's inequality tells us that the probability of X deviating from its mean by more than 20 units is at most 1/4 or 25%.

Remember this

Chebyshev's inequality is useful for proving the weak law of large numbers and can be applied to any probability distribution with defined mean and variance.

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

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