I never quite got the hang of this during my entry stat course and it has been bugging me for a long time now.
Lets assume I'm trying to find the focal length of a concave lens. Using a mockup formula for f, lets say:
f = D*x/y
where x , y, and D are measurements done with calipers with "precision" of 1mm each. Now I continue my experiment and make 10 different measurements for x, and 10 for y and compute 10 values for my f.
I want to present one final value for f and an "error" associated with that value. Do I use the mean value of my 10 f's as my final value? what do I use as a representation of "error"? Do I use the STD of mean for my 10 values or do I propagate the 1mm errors from my measurement and then use them to compute a weighed mean with associated error?