Computing the Standard Deviation

Fundamentals of Social Statistics


The standard deviation of a sample can be computed using the following equation:

standard deviation formula

  • Where s is the standard deviation
  • is the deviation score
  • N is the number of elements in the sample

To apply the formula, you will need to take the following step:

    1. Prepare a table with the first column being the scores (X)
    2. In the cell just below the list of scores, compute the sum of the scores (ΣX)
    3. Establish the number of elements in the sample (N)
    4. Compute the mean (X-bar)
    5. Create a second column of Deviation Scores, where you subtract the mean from each score (X-X-bar)
    6. Create a third column where you square the deviation scores X - bar-X squared
    7. In the cell just below the deviation scores, compute the sum
    8. Compute the degrees of freedom (N-1)
    9. Divide the sum of the squared deviation scores by the degrees of freedom to get the variance (s-square)
    10. Take the square root of the variance to get the standard deviation (s)

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Last Modified:  02/18/2019

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