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How to find the average value of several measurement results if we know their statistical and systematics uncertainties? There might be that there is no such thing as best way to do it, but it would be helpful to know how is this done in different areas of physics/science.

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"the standard way to..." (emphasis added) Which one? Especial with regard to the systematics you have to take care to be sure you understand how the uncertainty would effect your result. –  dmckee May 11 '12 at 15:28
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