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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Median versus Mean Averaging
From: Fred Hebard
Date: 2019 Oct 28, 08:59 -0400
On Oct 27, 2019, at 22:02, Bill Morris <NoReply_Morris@fer3.com> wrote:

I'm not a mathematician and have an uncertain grasp of statistics having once thought them to be a form of contact adhesive, but can say with the conviction of the possibly ill-informed that taking the median ensures that less weight is given to outliers.

Dear Bill,

I disclaim any grasp of statistics, but do use them in my work.

The mean is highly dependent on the distribution of observations.  If the distribution is skewed from the notorious bell-shaped curve, with more observations on one side of the the peak of the curve, then the mean does not accurately reflect the most likely location of an observation.  Outliers can skew a distribution.  The median is a more accurate measure than the mean in many instances of skewed distributions.  Without skewing, I believe (ie, I’m guessing) the mean is more accurate, especially with low numbers of observations

So!!! If the distribution of observations with a bubble sextant is bell-shaped, the mean is more accurate.  The mean would, of course, be harder to calculate than the median, which may be the reason the median was used in the first averaging instruments. </speculation>

Fred Hebard

On Oct 27, 2019, at 22:02, Bill Morris <NoReply_Morris@fer3.com> wrote:

I'm not a mathematician and have an uncertain grasp of statistics having once thought them to be a form of contact adhesive, but can say with the conviction of the possibly ill-informed that taking the median ensures that less weight is given to outliers.

And, mathematicians, how does continuously integrating as in the SOLD and Hughes Marine Bubble sextant, compare with averaging sixty observations two seconds apart?

Bill Morris

Pukenui

New Zealand

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