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Peter, you wrote:
"The next column shows the difference, and at the bottom of that column
the standard deviation is displayed: 0.7.  Excel file attached.

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

Your result, 0.7, is just right. It's not 1.22, because the "step size" for
this random walk is not constant. In a textbook random walk, you would have
N steps of equal size A. Then the expected distance after N steps is
A*sqrt(N). In the case of adding up numbers rounded to the nearest whole
number, the step size is 0.5 at most, but it's not constant and, on average,
it's smaller. In fact, what we need is the standard deviation of a uniform
distribution one unit wide ("uniform" since the fractional difference can
fall anywhere in the range from -0.5 to +0.5 with equal probability) and
that happens to be 0.288. And 0.288*sqrt(N) with N=6 is 0.7 just as you
found. It works. Now in a navigation problem things are rarely this simple,
so you couldn't directly apply this result, but the general principle is the
same.

 -FER


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