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See also: Statistical descriptions of model outputs, Variance, Range, Inter-percentile range, Mean deviation (MD)
Standard deviation is calculated as the square root of the variance. In other words:
It has the advantage over the variance that it is in the same units as the output it refers to. However, it is still summing the squares of the distances of each generated value from the mean and is therefore far more sensitive to outlying data points that make up the tails of the distribution than to those that are close to the mean.
The standard deviation is frequently used in connection with the Normal distribution. Results in risk analysis are often quoted using the output's mean and standard deviation implicitly assuming that the output is Normally distributed, and therefore:
the range x - s to x + s contains 68% or so of the distribution
the range x - 2s to x + 2s contains 95% or so of the distribution
Some care should be exercised here. The distribution of a risk analysis output is usually skewed and rarely normally distributed, so these assumptions do not then follow at all. However, Tchebysheff's rule provides some weak interpretation of the fraction of a distribution contained within k standard deviations.