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    Re: Averaging
    From: Chuck Taylor
    Date: 2004 Oct 19, 11:11 -0700

    George Huxtable wrote, concerning the concept of
    averaging observed sextant altitudes over time:
    "But I don't see how you would apply that
    technique to a quantity that was changing
    systematically, in the way that observed altitudes
    change rather steadily with time (either
    increasing or decreasing), with a bit of random
    scatter superimposed."
    Alex Eremenko commented:
    "To reduce random independent errors in a
    measurement of a quantity that changes linearly
    (or does not change at all), average is the proper
    thing to compute."
    The question is, "Does it make sense to average
    a quantity that is varying systematically over
    time, such as observed sextant altitudes?"
    We are talking about two components of variation,
    one systematic and one random. As Alex pointed
    out, averaging is certainly useful in eliminating
    random variation when there is no systematic
    variation. I would argue that it also makes sense
    when the magnitude of the random variation
    overwhelms the magnitude of the systematic
    variation, such as might occur at sea in rough
    weather on a relatively small vessel.
    Peter Fogg proposed a method that in effects
    allows one to average observations with variation
    taken into account:
    "...the process for averaging sights is simple and
    effective. As many sights as possible taken over
    about 5 minutes of time are plotted. Time is the
    horizontal axis, observed altitude on the
    vertical. The slope of this group of sights either
    rises; obs to the east, or descends; to the west.
    This slope is then compared to a calculated line,
    which is then best fitted to the slope of sights.
    Any extreme outliers are disregarded (probably
    best, although it goes against ideal statistical
    practice). Simple and effective."
    This gives you the best of both worlds, with the
    averaging done visually. As Jim Thompson pointed
    out, this is quite easy to do with a computer
    spreadsheet. The only issue is converting
    altitudes and times to decimal fractions.
    Chuck Taylor
     47d 55' N
    122d 11' W
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