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    Re: R: Averaging
    From: Bill B
    Date: 2004 Oct 18, 19:28 -0500

    Similar input to Federico's, but from the vantage point of
    marketing-research test instrument design.
    If, for example, I have two categories:
      Strongly agree
      Strongly disagree
    I am forcing respondents to one extreme or the other and they may not belong
    there.  Let's assume I have a population that has no strong opinion on the
    If I add a midpoint (odd number) possibility:
      No opinion
    and the vast majority choose it, then what appeared to be a polarized
    population becomes one with no strong opinions. But I may be comparing
    apples to oranges.
    Let's try a cel nav example (Assuming perfect sextant and operator). If I do
    a sight 2 minutes before LAN, 2 minutes after LAN, and average them I have a
    point on the midpoint of a chord (a straight line segment) from those two
    altitudes and below the actual LAN altitude on the arc.  If I add an
    observation at LAN, I move altitude closer to the arc and reality.  The more
    observations, the closer I get to approximating a position on the arc
    instead of on the chord.
    Since the sextant and operator are not perfect, the more observations I
    average the less affect one poor sight will have on the average.
    Once I get a lot of numbers in the average, I would guess (and it is only a
    guess) the odd vs. even would have less affect.
    > George,
    > The explanation I've found for this recommendation is that this way you
    > can consider the central value of the odd series (i.e. the so called
    > median) which is definitely less affected by abnormal values than the
    > average value.
    > This is a criterion that I also remember from my statistic course at
    > university.
    > Hope this can help.
    > Federico
    > -----Messaggio originale-----
    > Da: Navigation Mailing List [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM]
    > Per conto di George Huxtable
    > Inviato: domenica 17 ottobre 2004 23.45
    > Oggetto: Re: Averaging
    > I have read, here on Nav-l and elsewhere, the recommendation that when
    > averaging observations, it's best to take an odd, rather than even
    > number of them.
    > I've no idea why. Can anyone explain?
    > George.
    > ================================================================
    > contact George Huxtable by email at george---.u-net.com, by phone
    > at 01865 820222 (from outside UK, +44 1865 820222), or by mail at 1
    > Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    > ================================================================

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