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Ok, I'm sure this is simple, yet I'm confused.

Lets say my goal is to obtain an average concentration C=N/V so I take a number of N and V readings with errors:

$N_1=50\pm2, V_1=100\pm4$
$N_2=102\pm2, V_2=205\pm4$
$N_3=52\pm2, V_3=99\pm4$

Now if I remember correctly the standard deviation s propagates to C with

$s_{C} = \sqrt{(\frac{\partial{C}}{\partial{N}}s_N)^2+(\frac{\partial{C}}{\partial{V}}s_V)^2}$

But now how do I get the average with a meaningful total standard deviation? Or should I approach this in a different way altogether?

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up vote 0 down vote accepted

Compute $C_1$, $C_2$, $C_3$ as well as $s_{C_1}$, $s_{C_2}$ and $s_{C_3}$ separately, using the formula you have given. Next, compute the mean $\overline{C} = \dfrac{C_1+C_2+C_3}{3}$, and use the formula you have given to determine the standard deviation $s_{\overline{C}}$.

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