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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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