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The Complete Idiot's Guide to Statistics, 2nd Edition by Robert Donnelly

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Chebyshev’s Theorem

Chebyshev’s theorem is a mathematical rule similar to the empirical rule except that it applies to any distribution rather than just bell-shape, symmetrical distributions. Chebyshev’s theorem states that for any number k greater than 1, at least
127percent of the values will fall within k standard deviations from the mean. Using this equation, we can state the following:
◆ At least 75 percent of the data values will fall within two standard deviations from the mean by setting k = 2 into Chebyshev’s equation.
◆ At least 88.9 percent of the data values will fall within three standard deviations from the mean by setting

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