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    A puzzle
    From: Frank Reed
    Date: 2008 Jun 05, 10:29 -0400

    Here's a little math puzzle, related to celestial navigation calculations.
    
    Suppose I take three angles which have been rounded to the nearest tenth of
    a minute, and I add them up. What is the error in the sum? Specifically,
    what is the expectation value of the error? Or if you prefer, what is the
    standard deviation of the error? I will offer my "guess": the standard
    deviation of the error is 0.05 minutes of arc (a twentieth of a minute of
    arc) exactly. Please assume that the angles *before* rounding have no
    intrinsic error.
    
    As an example, I have these angles:
    43.681221'
    12.066312'
    3.625021'
    I add these numbers up, and get some answer. Now I round them to the nearest
    tenth of a minute of arc:
    43.7'
    12.1'
    3.6'
    If I add up these rounded numbers, the sum will differ from the previous one
    by a small amount. Now I do this sort of calculation a large number of
    times. What is the standard deviation of the difference between the two sums
    (exact and rounded)?
    
     -FER
    PS: busy, busy for the next several days. I won't have much time to post...
    
    
    
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