Say we use a ruler to make a measurement of the width of a block of wood. We get some value like
4.2 +/- 0.1 cm, where the error is our estimated error of our ruler's precision. Now we have four new individuals measure the same block of wood, and two of them obtain
4.5 +/- 0.1cm and two obtain
4.2 +/- 0.1 cm. If we take the mean of these five measurement we obtain
4.32 +/- 0.16 cm, where I'm ignoring significant figures in this example and the uncertainty is the standard deviation of the samples. Now, in stating the total uncertainty for the width of the block of wood, should I combine the 0.16 in quadrature with the 0.1, or should I propagate the error of each measurement through the standard deviation formula and obtain an uncertainty on my uncertainty, like
0.16 +/- alpha, where alpha is the propagated uncertainty value? Or perhaps I should ignore the standard deviation of the measurements and use the classic 0.1/sqrt(5)---but this is silly given the spread of our measurements. This seems like a simple question but I can't seem to find two sources that agree on the matter (har har).
Thanks for any help.