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Frank wrote:
> Your result, 0.7, is just right ...
> ... what we need is the standard deviation of a uniform
> distribution one unit wide ... and
> that happens to be 0.288. And 0.288*sqrt(N) with N=6 is 0.7 just as you
> found. It works.

Thanks to Frank (and Bill Noyce and Alex) for throwing much
appreciated light on this statistical question: the extent of error
when adding together rounded values, in this case six.

It began when Alex claimed: "the errors will accumulate", which was
later qualified to: "They will do both things: cancel but still
accumulate" which seemed difficult but it turns out that this is
indeed so.  Kind of.

In the example using Bennett tables they mostly cancel out, but
accumulate to the extent that an error, on average, of  0.7 of a whole
number can be expected when adding 6 rounded values, compared to
adding values expressed to the nearest tenth.  Its a fairly modest
accumulation.

Actually, I prefer to think in terms of the result of my experiment:
that in 86% of a random sample, the error was within 1 minute of arc,
which seems quite a usefully practical result for a method that uses
values rounded to whole minutes of arc, rather than the more commonly
employed tenths.

Remember that more precise Bennett tables are freely available for use
with lunars.

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