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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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