Welcome to the NavList Message Boards.


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

Compose Your Message

Add Images & Files
    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
    | 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
    | 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
    | 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
    | (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.
    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

    Browse Files

    Drop Files


    What is NavList?

    Join NavList

    (please, no nicknames or handles)
    Do you want to receive all group messages by email?
    Yes No

    You can also join by posting. Your first on-topic post automatically makes you a member.

    Posting Code

    Enter the email address associated with your NavList messages. Your posting code will be emailed to you immediately.

    Email Settings

    Posting Code:

    Custom Index

    Start date: (yyyymm dd)
    End date: (yyyymm dd)

    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site
    Visit this site