# Square root of number of counts vs standard deviation of the mean?

I'm doing an experiment in radioactivity, where I measure the number of counts in a given time interval when a radioactive source is placed in front of a detector at a fixed distance. I repeat 3 times and take the mean number of counts. What is a better error value of the mean to use, $\sqrt{n/3}$, where $n$ is the mean number of counts, or the standard deviation of the mean?

I would have thought the sd of the mean was better, as it gives an experimental estimate of the error. However, my demonstrator has said that $\sqrt{n/3}$ is better, although they can't quite put into words why. Could it be because we know radioactive decays are Normally distributed in the central limit approximation follow a Poisson distribution hence the error will always be $\sqrt{n/3}$?

• What is the possibility that the underlying intensity could vary appreciably among the three replications of the experiment? Does "$n$" refer to the total of the three counts, the mean, or the individual counts? Are the counts measured accurately or is there some measurement error? Are you using raw counts or have you subtracted a background estimate? – whuber Nov 26 '14 at 19:59
• The underlying distribution shouldn't vary, as radioactive decay is a purely random process. $n$ refers to the mean number of counts (updated question). There will be some measurement error in the detector/amplifier. And this is without subtracting background radiation (which is pretty small compared to the counts when the sample is placed in front of the detector) – binaryfunt Nov 26 '14 at 23:44
• The $\sqrt{N}$ thing will presumably have come from the standard deviation of a Poisson count. However, @whuber's questions are to the point. – Glen_b Nov 27 '14 at 0:01
• Ok, so I now understand why $\sqrt n$, but is there a reason not to use the sd of the mean? Is it because as $n$ goes to $\infty$ the error goes to 0? – binaryfunt Nov 27 '14 at 23:16
• Where you ask "What is a better error value to use", what is the purpose? What are you attempting to estimate? – whuber Dec 1 '14 at 15:56