Statistics Fundamentals: Chebyshev’s Inequality

​From Russian mathematician Pafnuty Chebyshev. It states that for any distribution with a finite variance: The proportion of the observations within “k” standard deviations of the arithmetic mean is (1 – (1/k2)).
 
The simplification of this statement has proved that a two-standard deviation interval around the mean must contain at least 75% of observations, and three-standard deviations must contain 89% of the observations. For instance, if you put 3 for “k” in the formula above, you receive (i.e. 1-(1/32) = 89%).