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Standard deviation as a percent?

  1. Oct 9, 2014 #1
    Say if I have a sample space 2,3, and 5. I want to find by what percent points deviate from the mean. So I would take the standard deviation as follows.

    2+3+5 / 3 = 3.33

    (2-3.33)^2 + (3-3.33)^2 + (5-3.33)^2 / 3 = 1.55

    (1.55)^(1/2) = 0.775

    So we get a standard deviation of 0.775. So how do I turn the standard deviation into a plus or minus percentage?
     
  2. jcsd
  3. Oct 9, 2014 #2

    mathman

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    Step 1: √1.55555 = 1.25
    Step 2: 100(1.25/3.33)
     
  4. Oct 9, 2014 #3

    FactChecker

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    It's important that you say that the three points, 2, 3, and 5 are equally likely results. That is implied by your calculation of the mean = (2+3+5)/3, where the three points each have probability 1/3 of occurring.

    As @mathman points out, your calculation of the standard deviation is wrong. You divided by 2 instead of taking the square root. The correct value is 1.24722.

    You want to know what percentage of a sample will be within 1 standard deviation of the mean. That is between 3.33333 - 1.24722 and 3.33333 + 1.24722. (between 2.086 and 4.581. Only the results X=3 are in that range. That probability is 1/3 = 33.3%
     
    Last edited: Oct 9, 2014
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