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Standard Deviation

The most generally useful measure of dispersion with measurement data is the standard deviation (and the variance, which is simply the square of the standard deviation).  The standard deviation is the average deviation of cases around the mean.  The higher the standard deviation, the more spread out the data.  For a sample, it is calculated as:

 

Most cases fall within one standard deviation of the mean.  Under very special circumstances of normality, the standard deviation can be used to calculate exact percentages within certain ranges of the mean.  Since the standard deviation is calculated using the mean, any serious skew will make the standard deviation unreliable as a measure of dispersion — just as it will make the mean unreliable as a measure of central tendency.

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Last Updated: January 19, 2005