# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**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. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---