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
Famous quotes containing the words definition of, definition, population and/or values:
“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
—Walter Pater (1839–1894)
“The definition of good prose is proper words in their proper places; of good verse, the most proper words in their proper places. The propriety is in either case relative. The words in prose ought to express the intended meaning, and no more; if they attract attention to themselves, it is, in general, a fault.”
—Samuel Taylor Coleridge (1772–1834)
“I think that cars today are almost the exact equivalent of the great Gothic cathedrals: I mean the supreme creation of an era, conceived with passion by unknown artists, and consumed in image if not in usage by a whole population which appropriates them as a purely magical object.”
—Roland Barthes (1915–1980)
“Our first line of defense in raising children with values is modeling good behavior ourselves. This is critical. How will our kids learn tolerance for others if our hearts are filled with hate? Learn compassion if we are indifferent? Perceive academics as important if soccer practice is a higher priority than homework?”
—Fred G. Gosman (20th century)