- #1
gnegnegne
- 12
- 1
In a lab experiment we had to measure some angles. Every angle measure is the difference between two angular positions and the instrument we used had a resolution of 1', so the uncertainty due to the instrument is $$\sigma_{instr}=\sqrt2'=0.02357... deg$$.
We measured the same angle a few times and we obtained values such as $$\theta_1=60.03 deg, \theta_2=60.00 deg, \theta_3=59.97 deg$$
The mean is 60 deg and the standard deviation of the mean is $$\sigma_{stat}=0.0173... deg$$.
What should I consider as the final uncertainty of the measure? The highest uncertainty? Or the sum of squares? I would consider the sum of squares because the uncertainties are independent, but our professor told us that the highest includes the other, and I haven't really understood why.
We measured the same angle a few times and we obtained values such as $$\theta_1=60.03 deg, \theta_2=60.00 deg, \theta_3=59.97 deg$$
The mean is 60 deg and the standard deviation of the mean is $$\sigma_{stat}=0.0173... deg$$.
What should I consider as the final uncertainty of the measure? The highest uncertainty? Or the sum of squares? I would consider the sum of squares because the uncertainties are independent, but our professor told us that the highest includes the other, and I haven't really understood why.