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The weighted mean

The weighted mean m is
m \eq
{\sum_{i=1}^N \ w_i^2 d_i \over
 \sum_{i=1}^N \ w_i^2
 }\end{displaymath} (7)
where wi2>0 is the squared weighting function. This is the solution to the $\ell^2$ fitting problem $ 0 \approx w_i (m - d_i)$;in other words,
0 \eq {d \over dm} \ \sum_{i=1}^N \ [w_i(m - d_i)]^2\end{displaymath} (8)

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