In the case where X takes random values from a finite data set x 1, x 2, …, x N, with each value having the same probability, the standard deviation is The Cauchy distribution has neither a mean nor a standard deviation. has a mean, but not a standard deviation (loosely speaking, the standard deviation is infinite). The marks of a class of eight students (that is, a statistical population) are the following eight values:Ģ, 4, 4, 4, 5, 5, 7, 9. For a finite set of numbers, the population standard deviation is found by taking the square root of the average of the squared deviations of the values subtracted from their average value. Suppose that the entire population of interest is eight students in a particular class.
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