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    Re: A puzzle
    From: George Huxtable
    Date: 2008 Jun 5, 16:48 +0100

    Frank asked-
    
    | 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)?
    
    ==================
    
    Response from George-
    
    Following Lars Bergman's analysis in navlist 1438 (which confirmed the
    result of my earlier Monte Carlo simulation in 1433), I would make the
    standard deviation to be exactly .05'
    
    It isn't exactly a Gaussian distribution, of course, but it's near enough to
    one for that result to be meaningful.
    
    George.
    
    contact George Huxtable at george@huxtable.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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