How to Find the Standard Deviation

After finding an average, sometimes it's helpful to find the way other numbers and results are distributed around that average. Use the standard deviation to measure the size of that distribution. This calculation comes in handy for real-life applications such as determining grades and the results of case studies.

Things You'll Need

  • Set of numbers
  • Calculator
  • Paper
  • Writing utensil
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Instructions

    • 1

      Find the average of your set of numbers. This can be done by adding all your numbers together, and dividing the sum by the number of values. For example, if you had four numbers in your list, you would divide the sum of all numbers by four.

    • 2

      Subtract the average from each number in the original list. These new values are called "deviations from the average."

    • 3

      Use a process called root-mean-square (RMS) to find the standard deviation. To start this process, square all of the deviations individually.

    • 4

      After each value has been squared, add all the new values together.

    • 5

      Divide the sum by the amount of numbers in the original list.

    • 6

      Take the square root of this number; this will be your standard deviation value.

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