20 WORKING WITH SAMPLE DATA Since the units are in MPG, the sample standard deviation estimated from the group data is 3.96 MPG. For comparison, the actual standard deviation for the 67 cars reported is 3.71 MPG. Chebyshev's Theorem and the Empirical Rule Two applications using the mean and the standard deviation are given by Chebyshev's Theorem and the Empirical Rule. Chebyshev's Theorem is named after the Russian mathematician Pafnuty L'vovich Chebyshev who proved that a minimum percentage of data values fall within two bounds on either side of the mean. Stated specifically, Chebyshev proved that the minimum percentage of values lying within k (k > 1) units of standard deviation of the mean is given by the following formulation. Chebyshev's Theorem Regardless of the shape of distribution, the minimum percentage of values close to the mean is