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Table of Contents Univariate Data Measures of Variation Chebyshev's Theorem	Index
See also: standard deviation, 4-sigma test

Chebyshev's Theorem

The Russian mathematician P.L. Chebyshev (1821-1894) proved a theorem which is valid for any distribution of data:
 

For any number k greater than 1, at least 1-1/k² of the data will fall within k standard deviations of the mean.

This theorem produces a few useful rules:

• no information can be obtained on the fraction of values falling within 1 standard deviation of the mean
• at least 75% will fall within 2 standard deviations
• at least 88.8 % will fall within 3 standard deviations

Last Update: 2006-Jän-17