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I have a set of points whose positions are represented by 3D vectors. Each point has the associated weight in range from 0 to 1. The sum of all weights doesn't equal to 1.

How should the weighted mean point be calculated from the whole set of points?

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    Yes, you're right.2012-10-31

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The process is called normalization, and you simly divide each weight by the sum of all the weights: $w_i \rightarrow \frac{w_i}{\sum w_i}$ You can easily verify that the sum of the new weights is now $1$.

The mean vector is given by the sum: ${\bf{v}} = \sum w_i \bf{v}_i$

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    Probably yes. I think this should be correct. Thank you.2012-10-31