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Short answer: Depends. Ideally you want to use the "minimum-variance unbiased estimator" given your data and assuming both systematic and random errors. In some cases it won't matter when you average, but generally the bias and the variance may change. For example consider the formula: $$ c = \sqrt{a^2 + b^2} $$ If you want to calculate $c$, given ...


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If we have a function $y=f(a,b)$ and we have uncertainties $\sigma_a$ and $\sigma_b$ in its parameters, the uncertainty of $y$ is given by $$ \Delta y = \sqrt{\left(\frac{df}{da}\sigma_a\right)^2 + \left(\frac{df}{db}\sigma_b\right)^2 } $$ This formula is true if the two parameters are not correlated, as is the case for the velocity your are interested in. ...


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Unfortunately, the words such as uncertainty, resolution, accuracy, etc., are used in everyday language do not mean the same as in physics or in engineering, and because of that these concepts lead to confusion. Anyhow, there really are two completely different concepts frequently confused, namely accuracy and resolution. Accuracy is essentially the standard ...


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The first is correct and the second is diabolically wrong. People get the idea that Poisson errors mean you just take the square root of everything. No! The thing you take the square root of has to be an actual number of events. Any scaling factors are applied afterwards.


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Instead of fitting the function $y=f(\vec x)$ for fixed input parameters $\vec x$ a single time you could change the input parameters $\vec x$ according to your uncertainty model and perform multiple fittings. This yields a distribution of the fit coefficients. The distribution captures the uncertainty of your inputs. As nu pointed out in many software ...


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