# standard deviation

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## standard deviation

[′stan·dərd ‚dē·vē′ā·shən]
(statistics)
The positive square root of the expected value of the square of the difference between a random variable and its mean.

## standard deviation

see MEASURES OF DISPERSION.

## standard deviation

(statistics)
(SD) A measure of the range of values in a set of numbers. Standard deviation is a statistic used as a measure of the dispersion or variation in a distribution, equal to the square root of the arithmetic mean of the squares of the deviations from the arithmetic mean.

The standard deviation of a random variable or list of numbers (the lowercase greek sigma) is the square of the variance. The standard deviation of the list x1, x2, x3...xn is given by the formula:

sigma = sqrt(((x1-(avg(x)))^2 + (x1-(avg(x)))^2 + ... + (xn(avg(x)))^2)/n)

The formula is used when all of the values in the population are known. If the values x1...xn are a random sample chosen from the population, then the sample Standard Deviation is calculated with same formula, except that (n-1) is used as the denominator.

[dictionary.com].

["Barrons Dictionary of Mathematical Terms, second edition"].

## standard deviation

In statistics, the average amount a number varies from the average number in a series of numbers.
References in periodicals archive ?
Statistically, however, the concentrated parameters model provided a proper fitting to the experimental data in terms of quadratic deviation.
Rk] = 310 kNm and taking into account the mean quadratic deviation of moment resistance [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] = 2160 kNm, the probability of beam failure is:
5 cm, among the tested models, Midilli showed the best fit to the experimental data, with the highest coefficients of determination and the lowest mean quadratic deviations.

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