Chebyshev inequality

In probability theory, Chebyshev's inequality (also called the Bienaymé–Chebyshev inequality) provides an upper bound on the probability of deviation of a random variable (with finite variance) from its mean. More specifically, the probability that a random variable deviates from its mean by more than ${\displaystyle k\sigma }$ is at most ${\displaystyle 1/k^{2}}$, where ${\displaystyle k}$ is any positive constant and ${\displaystyle \sigma }$ is the standard deviation (the square root of the variance).