# Error Metric which incorporates both mean & standard deviation of data in euclidean space

For simplicities sake (the actually problem is more complex)...Let say I have a set of n 3d points, whose position move over time. For all pairs, I have calculated the mean and standard deviation of the euclidean distance between them.

I would like an error metric which incorporates the following two properties and I can use to "score" each pair in an attempt to find the "best".

1) Pairs of points which on average over time are "close" to one another are preferred i.e small mean -> low error

2) Pairs of points whose distance between them over time varies little i.e small standard deviation -> low error

Furthermore, I want to be able to weight the influence of each property.

And I am not sure of the mathematically correct way of combining these two properties.

Any help much appreciated.

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is this homework? one choice is: $\|(x-u)'S(x-u)\|$ –  Suvrit Jun 15 '12 at 8:49
No it is not homework. I think you have misunderstood the question, as your answer makes no sense in that context. –  Oracle3001 Jun 16 '12 at 15:06