[Therion] Handling of tape and backtape in survey data

[Olly Betts]

On Mon, Dec 27, 2021 at 05:04:20PM -0600, Bill Gee wrote:
> My question about significant digits is really related to how much
> precision can and should be carried through a calculation.  If compass
> readings are taken to four significant digits, then the mean of two
> such numbers is really only good to about three and a half significant
> digits.

That seems wrong to me - we expect the mean to have *better* accuracy
than the individual readings (otherwise one would want to avoid
averaging readings!)

Assuming independence (which may not an entirely valid assumption here
admittedly) and that both readings have the same standard deviation x,
then the s.d.  of the mean of 2 readings is x/sqrt(2) - or about
0.707*x.  I think that means you actually would expect to gain
log(1/sqrt(2))/log(1/10) or about 0.15 decimal significant digits from
taking the mean of two readings.  (And it's 1/sqrt(n) for n readings, so
if you average 100 independent readings then you'd expect to gain a
whole decimal significant digit.)

> Displaying more significant digits implies more precision
> that actually exists.

Right, but that argues for suitably presenting reported values, not for
rounding intermediate values during the calculations.

> A compass reading even from a DistoX2 is
> probably accurate to only +/- 2 least significant digits.
> 
> https://en.wikipedia.org/wiki/Significant_figures

I'm not quite sure what "2 least significant digits" means, and that
wikipedia page doesn't seem to help.

But I think I get the gist, and indeed any instrument will have a limit
to its accuracy, especially so for anything you'd be likely to consider
taking underground.

Cheers,
    Olly