Error propagation and standard deviation

[Sral2018]

Hey there,
First time on this forums, looking forward to some interesting discussions :)
I am currently trying grasp the concepts of error propagation and standard deviation in relation to experimental physics. I have some data set and i want to determine the difference between the measured and theoretical values including errors and how reliable my reading are. My problem is how do i include these errors in the standard deviation?

 

[Dr Dr news]

You might check Kline and McClintock's 1953 paper on uncertainty analysis. It is a standard in the field.

 

[Dale]

There is also the NIST guidelines which are a little more up to date.

https://www.nist.gov/sites/default/files/documents/2017/05/09/tn1297s.pdf

 

[f95toli]

Or the GUM if you want the official guide

https://www.bipm.org/en/publications/guides/gum.html

Note that the GUM is actually quite readable so it is worth a look,