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.


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

Last updated: 2003-05-06