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I have the list of experimental values: $$\{w_i \pm \Delta w_i\},$$ where $w_j$ is a mean value and $\Delta w_i$ is an error.
I want to calculate the second list $\{a_i \pm \Delta a_i\}$ according to the rule $$a_i = \frac{w_i / A_i}{\sum_j w_j / A_j},$$ where $A_i$ is some constant for $i$.
How to define errors $\Delta a_i$? Is it the right way?
$$\Delta a_i = \frac{1}{A_i} \frac{\Delta w_i |\sum_j w_j/A_j| + |w_i|\sum_j \Delta w_j/A_j}{(\sum_j w_j/A_j)^2}$$
According to link from foregoing comment $a_i$ measurments are inderect, so errors are
$$\Delta a_{i}=\sqrt{\sum_{k}\left(\frac{\partial a_{i}}{\partial w_{k}}\Delta w_{k}\right)^{2}}.$$
After calculations it yields $$\Delta a_{i}= \frac{1}{\left(\sum_{j}\frac{w_{j}}{A_{j}}\right)^{2}A_{i}}\sqrt{\sum_{k}\left( \left[\delta_{ik}\sum_{j}\frac{w_{j}}{A_{j}}-\frac{w_{i}}{A_{k}} \right] \Delta w_{k} \right)^{2}}$$
