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 ?
Z], converges to the parameter that it estimates, the population standard deviation, [[sigma].
In calculating sample size, the effect size and population standard deviations have to determined (and justified) by the scientists with the help of previous literature or their own preliminary data, while the power and significance level are taken as 80% and 95% respectively as a convention.
However, with knowledge of the population standard deviations of the parameters that make up the SIG, a 95% confidence interval (CI) for SIG can be indirectly derived using methods of static (Monte Carlo) simulation.
But, if we know the value of the population standard deviation, we use the finite correction factor formula because it is quicker.
For the independent samples t-test the ES index is referred to as 'd' and is calculated by finding the difference between means and dividing by the within population standard deviation.
In the previous section, we assumed that we knew the population standard deviation and we wanted to estimate the population mean using sample data.

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