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A constant k needs to be calculated including its gaussian error. $k = f_{(u,t)}$

$k_i$ can be calculated with the values and errors of $u_i$ and $t_i$ and their respective errors.

Main issue is that i can not calculate the mean value $\bar{k}$ of $k_i$'s without loosing error information. There is some error attached to using $f_{(u,t)}$ the values $k_i$ appears not to be constant although they should be - a function $g_{(u,t)}$ wich does not have that problem is not available.

If i just calculate $\bar{k}$ and transport the error normally using gaussian error translation, my error explodes beyond reason, multiple measurements should make my error smaller.

If i use the standard deviation error, the error information of individual $k_i$ values is lost and my error is so small that i cant sleep at night.

I dont even know where to start on solving this problem.

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I don't know if I understand your question. You have a value $k$ which you can compute if you know $u$ and $t$. Through a series of experiments you find a number of pairs $\{u_i,t_i\}$ from which you can find $k_i$. But there is uncertainty in the measurements of $\{u_i,t_i\}$, which lead to uncertainty in the computed $k_i's$? –  user16124 Mar 6 '12 at 17:57
    
Yes, and now i have a set of $k_i$ values with uncertainties. I want to get to a $\bar{k}$ with uncertainty and dont know how to do that. I need $\bar{k}$ to not only pay respect th the uncertainty of of $k_i$ values, but also pay respect to the drift of the $k_i$ values. in the end i want to write something like $\bar{k} = (20 \pm 3) \cdot 10^{-3} seconds$. –  Johannes Mar 7 '12 at 9:51

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