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Thread: Standard deviation

  1. #1 Standard deviation 
    Forum Masters Degree thyristor's Avatar
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    How come standard deviation is sometimes calculated
    http://www.cs.utexas.edu/users/scott...tandardDev.gif
    and sometimes
    with the same formula but n instead of n-1 in the denominator?[/tex]


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  3. #2 Re: Standard deviation 
    . DrRocket's Avatar
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    Quote Originally Posted by thyristor
    How come standard deviation is sometimes calculated
    http://www.cs.utexas.edu/users/scott...tandardDev.gif
    and sometimes
    with the same formula but n instead of n-1 in the denominator?[/tex]
    The population standard deviation is calculated with "n". It is the standard deviation of a random variable defined on a domain of n points.

    The calculation that uses "n-1" is the sample standard deviation. It is the best unbiased estimate of the standard deviation of a population, possibly infinite, based on a sample. The sample standard deviation is itself a random variable.

    This is usually explained in terms of variance, variance being the more fundamental quantity, the square root of which is the standard deviation. See the discussion of population variance and sample variance in this Wiki article.

    http://en.wikipedia.org/wiki/Variance


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  4. #3  
    Forum Professor river_rat's Avatar
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    As Dr Rocket said, if you try to estimate the std deviation using the 1\n version, after you have first estimated the mean, you will on average underestimate the thing you are trying to calculate.

    [edit - fixed typo]
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  5. #4  
    Forum Ph.D.
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    A simple explanation:

    If you know the mean exactly, use 1/n. If you use the sample average to estimate the mean, use 1/(n-1) to take into account the uncertainty in the mean.
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  6. #5  
    Forum Masters Degree thyristor's Avatar
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    Ok, thanks for your replies.
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