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The standard deviation ($$SD$$) is computed by determining the difference between each score ($$X$$) and the mean ($$M$$), squaring those differences, finding the mean of the squared differences, and finally taking the square root of that mean. The formula is: $$SD = \sqrt{\frac {\sum (X-M)^2}{N}}$$.

Formula for the Standard Deviation

When calculating the standard deviation to simply describe a sample, the sum of squared differences is divided by $$N$$. However, when the goal is to estimate the standard deviation of the broader population, researchers divide by $$N - 1$$ to correct for the tendency of a sample's standard deviation to underestimate the population's true variability.

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