# NavList:

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

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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
topic.

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.

Bill

> 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-----
> 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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