APPENDIX B. AN INTRODUCTION TO ERROR ANALYSIS measured quantity a is given by δf a = ± ∂f ∂a ² δa, with similar expressions for the uncertainty due to b , c , etc. The second premise is that if the measured values a , b , c , etc. are uncorrelated the uncertainty in f from each adds in quadrature as follows ( δf ) 2 = ( δf a ) 2 + ( δf b ) 2 + ( δf c ) 2 + ... Uncertainties are uncorrelated when they are completely independent of each other. For example if you measure the mass and acceleration of an object to determine the force on it, your measurement of mass should have an uncertainty that has nothing to do with the uncertainty in your measurement on acceleration. An example of correlated uncertainties would be if you measured the radius of a circle and then doubled that to get a value of diameter that you consider a “measured” value - any error in the measurement of the radius would then produce the same relative error in the recorded value for the diameter, so these uncertainties are
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