Definition of Standard deviation

A computed measure of variability indicating the spread of the data set around the mean.

The square root of the variance. A measure of dispersion of a set of data from their mean.

1. the most used measure of dispersion, its value tells how closely the values of a data set are clustered around the mean.
Note: the larger the value, the larger the range around the mean.
2. used as a measure of risk to make comparisons among investments.
Note: also as the same with risk, the higher the standard deviation, the higher the risk.

(s,BESD, ) The standard deviation is a statistical measure of precision. The best estimate of the standard deviation s for small data sets is calculated using

where xi is the measurement from the i-th run, x-bar is the mean of all the measurements, and N is the number of measurements. For very large data sets, the standard deviation is the root-mean-square deviation from the true mean, and is usually written as to distinguish it from the best estimate standard deviation s used for small data sets.

The standard deviation (this term was first used by Pearson, 1894) is a commonly-used measure of variation. The standard deviation of a population of values is computed as:
= [ (x_i-µ)²/N]^1/2
where
µ is the population mean
N is the population size.
The sample estimate of the population standard deviation is computed as:
s = [ (x_i-x-bar)²/n-1]^1/2
where
xbar is the sample mean
n is the sample size.
See also, Descriptive Statistics Overview .

Like variance, the standard deviation (SD) is a measure of variability. Unlike variance which is expressed in squared units of measurement, the SD is expressed in the same units as the measurements of the original data. If a distribution's SD is greater than its mean, the mean is inadequate as a representative measure of central tendency. For normally distributed data values, approximately 68% of the distribution falls within ± 1 SD of the mean, 95% of the distribution falls within ± 2 SDs of the mean, and 99.7% of the distribution falls within ± 3 SDs of the mean. SD should not be confused with the standard error.

standard deviation

A parameter that indicates the way in which a probability function is centered around its mean and that is equal to the square root of the moment in which the deviation from the mean is squared. Used to describe sets of values to determine how far the value varies from the arithmetic mean or average.

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(Statistics) A measure of the variability of a series of data about its mean value. The standard deviation is equal to the square root of the Variance, from which it is derived, and measures the sum of the differences between a series' values and its mean. The standard deviation for a large data set (the population standard deviation) is calculated as: s (sigma) = (Sum(xi :  x)2/n)-2 (sigma) = (Sum(xi :  x)2/n)-2; where: xi is an individual observation; x is the mean of all observations; and n is the number of observations. xi is an individual observation; x is the mean of all observations; and n is the number of observations. For smaller data sets (typically less than 50) the sample standard deviation (s) is calculated by replacing n with n: 1 in this equation.

The most widely used measure of dispersion of a frequency distribution, equal to the positive square root of the variance.

The statistical calculation denoting the variability of responses to an exposure. One standard deviation incorporates 68% of the responses while two standard deviations incorporates 95% of the responses.

a statistical measure of variance. Ninety-five percent of a range of values lie within 2 standard deviations of a mean value.

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Noun
1. the square root of the variance
(hypernym) variance
(classification) statistics