Given a random variable X with finite mean μ and variance σ2, then for any k ≥ 0 What Chebyshev's Inequality gives
P(|X - μ| ≥ k) ≤ σ2/k2Letting k be n > 1 standard deviations, the probability that a measurement will be at least nσ away from the mean is 1/n2. For n = 2, the probability that a measurement will be at least two standard deviations away from the mean is 1/4, which means the the probability that a measurement will be no more than 2 standard deviations aways from the meain is 1 - 1/4 = 0.75.
This page last modified on 24 January 2006.