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# The standard deviation

The standard deviation is the sum of squared deviations (or errors) of a data set with respect to the mean divided by the number of data.

By far the most common formula for computing variance in a sample is: Where:

• s² = standard deviation
• X = value
• M = mean
• N = sample size

Since samples are usually used to estimate parameters, s² is the most commonly used measure of variance. Calculating the variance is an important part of many statistical applications and analyses. It is the first step in calculating the standard deviation.

## Example:

if your set is 1, 2, 3, 4, 6, 8 we can compute the standard deviation as follow:

 X Freq. M (X-M) (X-M)^2 1 1 4 3 9 2 1 4 2 4 3 1 4 1 1 4 1 4 0 0 6 1 4 2 4 8 1 4 4 16 24 6 34

• Sample size N = 6 (frequency)
• The mean : 24/6 = 4
• The sum of (X-M)^2 = 34
• 34/6 = 5.67