Cant find the error values correctly. Need Suggestions.

Question

I have 6 observational data. $L_1,L_2,L_3,L_4,L_5 $ and $ L$. Each of them have seperate error values $\delta L_i$ and $\delta L$. All of these data are numbers such as $1.38e36, 3.45e33, 9.61e41$, etc., their units are the same.When I make the summation I get $L_1+L_2+L_3+L_4+L_5 \approx L$. But I can't find any equality between $\delta L_1+\delta L_2+\delta L_3+\delta L_4+\delta L_5$ and $\delta L$

I tried standart error method which is where $f=L$, $a_i=L_i$

$\delta f= \sqrt{\sum (\frac{\partial f}{\partial a_i}\delta a_i)^2}$

Also I tried to use $\frac{\delta L_1*L_1+\delta L_2*L_2+\delta L_3*L_3+\delta L_4*L_4+\delta L_5*L_5}{L} \approx \delta L$

and also I tried

$\frac{\sqrt{(\delta L_1*L_1)^2+(\delta L_2*L_2)^2+(\delta L_3*L_3)^2+(\delta L_4*L_4)^2+(\delta L_5*L_5)^2}}{L} \approx \delta L$

or $\sqrt{\frac{(\delta L_1*L_1)^2+(\delta L_2*L_2)^2+(\delta L_3*L_3)^2+(\delta L_4*L_4)^2+(\delta L_5*L_5)^2}{L^2}} \approx \delta L$

Nothing is working well. So I cannot calculate $\delta L$. Any ideas or suggestions?

It might help to say what the value of $\delta L$ is? – Paul Nov 24 '23 at 15:36 — Paul, Nov 24 '23 at 15:36
for instance, $L = 7.38e40$ and $\delta L = 5.23e39$ – Ege Tunç Nov 24 '23 at 16:45 — Ege Tunç, Nov 24 '23 at 16:45

score 1 · Answer 1 · answered Nov 24 '23 at 14:39

It sounds like you really only have five observations and add them up to get the value for $L$. If that is correct, $\delta L$ is just the sum of the absolute values of the individual errors. In your example the errors have greatly different magnitudes so the sum will be dominated by the largest one.

Cant find the error values correctly. Need Suggestions.

1 Answers1