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    Re: Instumental error?
    From: Alexandre Eremenko
    Date: 2005 Apr 20, 16:41 -0500

    Dear George,
    
    1. For OUR purposes, division by 6 and division by 7
    are of course indistinguishable (sqrt{7/6}=1.08).
    
    2. But in general, there are two kinds of standard deviation.
    a) Population "standard deviation",
    sqrt(sum (x_j-x)^2/n) (where x is the average and n the number
    of observations),
    and the
    b) Sample standard deviation, similar formula but with n-1
    instead of n.
    
    In the problem of our type, when you want to
    estimate the unknown standard deviation of
    some "population" (sorry, this is a technical term),
    from a finite sample
    of this
    population, the right thing to use is the Sample
    standard deviation. (The difference between the two is non-negligible
    only for small samples).
    
    (My calculator actually has two separate buttons for these
    two kinds of standard deviation).
    The technical explanation of advantages of the
    "sample SD" in comparison with "population SD"
    is something I don't want to go into on this list.
    (Stated very briefly, and in technical language it
    is because the sample SD in an UNBIASED estimate for
    the actual SD, while population SD is BIASED).
    
    For details (which, I repeat, are IRRELEVANT for
    a practical navigator), see any good course of
    statistics) or type these words "sample standard deviation"
    and "population standard deviation" on the web.
    For example, http://www.quickmba.com/stats/standard-deviation/
    
    Besides, sample SD is larger than population SD,
    and I always want to be on the same side:-)
    
    On an earlier remark of Fred Hebbard
    (Tue Apr 19 2005 - 22:46:11 EDT )
    "I would prefer that the standard deviations
     be given to an extra digit".
    
    my question is "What for?" I mean what can be a possible
    use of this extra digit be?
    
    Alex.
    
    
    

       
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