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    Re: Raw data for bubble
    From: Peter Fogg
    Date: 2007 Mar 9, 16:36 +1100

    Alex wrote:
    
    > But if your goal is to know your position in the sea,
    > the average is not useless: it tells you your position.
    
    I guess this is true so long as the errors are truly random, so that
    given enough observations the positives and negatives can balance each
    other out. And then you need lots and lots of observations - the more
    the better for this exercise.
    
    In practice only a limited number of observations of the same body is
    usually possible, for a variety of reasons, so any outlier has a great
    chance to significantly skew the results of averaging, away from the
    actual position.
    
    An advantage of comparing the slope is that these outliers are
    immediately seen and discarded.
    
    In practice the sort of gross error that tends to crop up is writing
    down the wrong minute of time, while focusing on the seconds; or the
    wrong degree of altitude, while concentrating on the minutes. Taking a
    close look at the graphical analysis known as comparing the slope may
    enable the identification and rectification of such error, so good
    data has been created from bad. Averaging would have simply led to an
    erroneous result, particularly with few observations.
    
    Comparing the slope is a kind of averaging, since with even random
    errors the adopted line will bisect the negative and positive values.
    I think having a graphical solution is intuitively more useful than
    just a row of numbers - you can evaluate the sights made and shift the
    line of best fit to suit the data by eye in a way that no mathematical
    number crunching process can achieve quite as well. In effect you can
    nominate the importance given each sight; how close to the adopted
    line you allow it to sit, perhaps in accordance with your memory of
    how clearly and how well you remember that sight being made, as well
    as in light of how the other sights fit the line.
    
    Don't laugh! Often when making observations you think: yes, that went
    well, or the opposite; that one might have been a bit dodgy. In the
    end the sights have to fit the line and to some extent the resolution
    of this problem is best done intuitively, I think; and graphically, I
    am sure.
    
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