Propagation of Errors Even simple experiments usually call for the measurement of more than one quantity. The experimenter inserts these measured values into a formula to compute a desired result. Here, we list several common situations in which error propagion is simple, and at the end we indicate the general procedure. If you are faced with a complex situation, ask your lab instructor for help. Many types of measurements, whether statistical or systematic in nature, are not distributed according to a Gaussian.
Examples are the age distribution in a population, and many others.
The theorem In the following, we assume that our measurements are distributed as simple Gaussians. This partial statistical cancellation is correctly accounted for by adding the uncertainties quadratically. If y has no error you are done. This way to determine the error always works and you could use it also for simple additive or multiplicative formulae as discussed earlier. Also, if the result R depends on yet another variable z , simply extend the formulae above with a third term dependent on D z .