Error Analysis: Calculating Error from Radiation Counts

[hartraft]

Not sure if this is the best place for this post, if it isn't any recommendations would be appreciated.

My qustion concerns calculating the error from a set of radiation counts. I understand that the error in a single radiation count is $$\sqrt{N}$$ 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

 

[zli034]

Average of counts is the unbiased estimator for N in this case. So the estimator of square root of N is the square root of average counts. In other words, if you want to estimate the error you use square root of average counts, as population of the counts getting large we are able to reach the theoretical error measure. By comparing the theoretical error with measures of error got from experienced you can know how likely the experiment result to happen.