# 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) Commented 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... Commented 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.

However, you need to be very cautious about this sort of thing. For example, if both probes are plugged into the same receiver (box, USB port, whatever), there may well be systemic bias which is not zero-mean. Both probes could have the same bias, in other words.