Chebyshev's Theorem
mathcenter.oxford.emory.edu › site › math117This relationship is described by Chebyshev's Theorem: For every population of n values and real value k > 1, the proportion of values within k standard deviations of the mean is at least. 1 − 1 k 2. As an example, for any data set, at least 75% of the data will like in the interval ( x ¯ − 2 s, x ¯ + 2 s). To see why this is true, suppose a population of n values consists of n 1 values of x 1, n 2 values of x 2, etc. (i.e., n i values of each different x i in the population).