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Formulae for the standard deviation

Whilst it is not necessary to learn the formula for calculating the standard deviation, there may be times when you wish to include it in a report or dissertation.

The standard deviation of an entire population is known as σ (sigma) and is calculated using:

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Where x represents each value in the population, μ is the mean value of the population, Σ is the summation (or total), and N is the number of values in the population.

The standard deviation of a sample is known as S and is calculated using:

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Where x represents each value in the population, x is the mean value of the sample, Σ is the summation (or total), and n-1 is the number of values in the sample minus 1.