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standard deviation

   Also found in: Dictionary/thesaurus, Medical, Legal, Financial, Acronyms, Wikipedia, Hutchinson 0.04 sec.

In statistics, the average amount a number varies from the average number in a series of numbers.


(statistics)standard deviation - (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.

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

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For example, elementary-school students who have a teacher who performs in the top quartile of all elementary-school teachers learn 33 percent of a standard deviation more (substantially more) in math in a year than students who have a teacher who performs in the bottom quartile.
The standard deviation of each group was averaged from each subject's sum of strides at each speed conditions.
 
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