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hartraft

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My qustion concerns calculating the error from a set of radiation counts. I understand that the error in a single radiation count is [tex]\sqrt{N}[/tex] where N is the number of counts. My question is what happens if i have taken multiple counts with the intention of using an average.

For example if i have three counts of 225, 197 and 211 with errors of 15, 14, and 14 respectively, the average count is 211, what is the error? Do i use the standard method of combining errors even this these are all measurements of the same variable?

Any help would be appreciated