# How should I calculate uncertainty of measurement calculated as average of two measurements

I am measuring force with two channel transducer. Both channels (separately) of this transducer has been calibrated and I can calculate uncertainty of measurement for each of it. However I want to take average of both measurements as my final measured value - I think this should give me better value. How should I calculate uncertainty of that measurement?

• The error propagation formula is used in almost all contexts by physicists. Do you have a reason not to use it here? (It even is particularly simple for the average of two things) Oct 28, 2014 at 13:35
• This is almost a duplicate of physics.stackexchange.com/questions/29829/… , but since the (accepted) answer to that is incorrect... Oct 28, 2014 at 15:25

In the absence of other knowledge, the best you can do is average the readings and claim the undertainty is $\frac{1}{\surd2}$ times the quoted accuracy of each probe . This is based on the assumption (hope) that the two measurements are uncorrelated, so you're essentially performing a vector sum of orthogonal uncertainties.