# Standard deviation

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"].