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Arrghhh !!  Alex, for an expert on statistics you are proving remarkably diificult to convince about this. Averaging is NOT the best way to go because there is only one correct path that the celestial body traces over time, either (apparently) rising or falling.  Outliers, in this special case, are not helpful.  Exceptions to that line are simply errors.  An average that includes such an error has the potential to significantly drag the averaged reading towards that error, away from the other sights which well may be (more or less) correct.  

 

A much more useful technique is to compare a number of sights taken over a short period with THE FACT (albeit an approximation, since the movement is an arc) of that body's movement over the same period. One advantage is that outliers (gross errors) can be eliminated from consideration.  There is a benefit, I contend, to this being a matter of human judgement in this special case, rather than a mathematical technique devoid of reflection.  One reason for this is that the person doing the analysis is usually the person who observed the sight, so may already have an idea of which sights may be better or less so, depending on the conditions at the time.

 

In any case, the round of sights taken is thereby transformed into a picture, which our brains can better analyse than a row of numbers.  That picture can be very informative.  Typically, the derived altitude/time is better (more accurate) than any of the raw sights.

 

 

No.  The object of the exercise is greater accuracy.

 

Incidentally, your author's general argument in favour of micrometer over vernier sounds good.