Quick question about finding standard deviation

  1. rock.freak667

    rock.freak667 6,228
    Homework Helper

    [SOLVED] Quick question about finding standard deviation

    Now I know that [tex]\sigma=\sqrt{var(x)}[/tex]

    which simplifies to this expression : [tex]\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(x-\overline{x})^2}[/tex] can someone show me how they got such an expression?

    and in chemistry I have to use a standard deviation calculation to get out a problem. Now normally I would use the above equation but my notes tell me to use this equation:

    [tex]\sigma=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x-\overline{x})^2}[/tex]


    Which one is correct to use? and can someone tell me if this is correct [tex]c_v =\frac{\sigma}{\overline{x}}[/tex] where [tex]c_v[/tex] is the coefficient of variation
     
  2. jcsd
  3. mathman

    mathman 6,517
    Science Advisor
    Gold Member

    The definition of the st. dev. depends on whether or not the mean is the true mean or the average of the experimental data. For the true mean use 1/N, for the experimental average use 1/(N-1). If you take the average of the variance with the experimental mean and compare it to the average of the variance with the true mean, you will see they are equal.
     
  4. rock.freak667

    rock.freak667 6,228
    Homework Helper

    Oh I see now,thank you
     
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