How to Simplify Standard Deviation Sigma Percentage

The standard deviation calculation is a useful statistical tool showing how far a piece of data varies from the mathematical mean. The standard deviation is sometimes called a sigma. Scientists, sociologists, demographers and school teachers all use the standard deviation measurement. The number is calculated by taking each data point and subtracting the average of the data points from it, then adding those results and dividing by the number of data points. The standard deviation stated as a percentage is actually the relative standard deviation. Simplifying that percentage will make it into a whole number.

Things You'll Need

  • Set of data
  • Paper
  • Pencil
  • Statistical calculator (optional)
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Instructions

    • 1

      Write the relative standard deviation, or the standard deviation written as a percentage, as a fraction. For example, if the standard deviation is 5.3 percent, write it down as 5.3/100.

    • 2

      Divide the standard deviation by 100 to reduce the fraction. Following our example, the calculation is 5.3 divided by 100. This gives us the number .053.

    • 3

      Multiply this number by the average of the data points. To calculate the standard deviation, it was first necessary to find the mathematical average of all the data points, then calculate each data point's variance. Take the mathematical average and multiply by the number you just calculated. For our example, imagine the average of the data points was 63.6. You would then multiply .053 x 63.6 to get 3.37, which rounds to 3.4.

    • 4

      State the standard deviation as a whole number. In this case, the simplified percentage is 3.4, giving you a standard deviation of 3.4. To state the results of a test, you would say that you have a confidence of plus or minus 3.4 in your results.

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