# standard deviation

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Related to standard deviation: variance

## 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 ?
If we use a shorter timeframe of five years, the standard deviation will be lower at 21 percent, but the average annual returns will also be lower at 5.17 percent, which is lower than current bond yield of 5.5 percent, resulting in negative Sharpe ratio.
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It is consistent with the value of standard deviation of that series which is about 0.0762 Hz and it also reveals the limitation of the built meter.
In this case, the standard deviation of each picture was determined and classified.
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"The increased mortality in warmer summers was entirely due to anomalies, whereas it was the long-term average differences in the standard deviation of summer temperatures across ZIP codes that drove the increased risk," researchers wrote.

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