Chebyshev's theorem

Chebyshev's theorem is a name given to several theorems proven by Russian mathematician Pafnuty Chebyshev

• Bertrand's postulate
• Chebyshev's inequality
• Chebyshev's sum inequality
• The statement that if the function $\scriptstyle \pi (x)\ln x/x$ has a limit at infinity, then the limit is 1 (where π is the prime-counting function). This result has been superseded by the prime number theorem.

The proportion (or fraction)of any set of data lying with K standard deviations of the mean is always at least 1-1/^K, Where K is any positive number greater than 1.