# NavList:

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

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Re: Lunars using Bennett
From: Bill Noyce
Date: 2008 Apr 7, 09:34 -0400

```>  If I've understood correctly, the standard deviation should
>  approximate 1.22 (0.5xsqrt6)."

As Frank explained, you need to multiply by the SD of the input
numbers, not their maximum possible error.

> The Wikipedia article was also interesting, if potentially confusing.
> I was struck by:
> "As expected of a random walk with equally probable outcomes, the
> expected value will come out to zero."
> which seems to imply that, relating this back to our example, that the
> equally probable average difference of 0.5 (between a value rounded up
> or down) will ... tend to cancel themselves out!  No doubt I have
> misunderstood.

This simply means that the probability of the sum being too large by
some amount is equal to the probability of the sum being too small
by the same amount.  You can visualize the results of a bunch of
experiments forming a bell curve.  Saying the expected value is zero
just means that's where the middle of the bell curve falls -- but it doesn't
say anything about how wide the curve is, nor how far its tails extend.

-- Bill

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