Definition of Population Values
Let X be a random variable with mean value μ:
Here the operator E denotes the average or expected value of X. Then the standard deviation of X is the quantity
That is, the standard deviation σ (sigma) is the square root of the variance of X, i.e., it is the square root of the average value of (X − μ)2.
The standard deviation of a (univariate) probability distribution is the same as that of a random variable having that distribution. Not all random variables have a standard deviation, since these expected values need not exist. For example, the standard deviation of a random variable that follows a Cauchy distribution is undefined because its expected value μ is undefined.
Read more about this topic: Standard Deviation
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—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“Although there is no universal agreement as to a definition of life, its biological manifestations are generally considered to be organization, metabolism, growth, irritability, adaptation, and reproduction.”
—The Columbia Encyclopedia, Fifth Edition, the first sentence of the article on “life” (based on wording in the First Edition, 1935)
“Like other cities created overnight in the Outlet, Woodward acquired between noon and sunset of September 16, 1893, a population of five thousand; and that night a voluntary committee on law and order sent around the warning, “if you must shoot, shoot straight up!””
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