I recently did a laboratory exercise where we had an amount of silver containing two isotopes. Silver with 108 and 110 neutrons, respectively. Using sensors and software, we measured the amount of emitted electrons from the silver in question. We made a measurement every 5 seconds for 900 seconds. By plotting emissions against time, we got a plot looking as follows:
But the problem is that we need to have error bars on our measurements, and it's been a year since I studied a statistics course, so I'm more than a little rusty. The error bars should be ± 1 standard deviation, I believe.
As far as I can recall, since this is about radioactive decay, generally speaking, a Poisson Distribution is a pretty good fit. The Poisson distribution is pretty neat in that the variance of the distribution is the same as the mean. But of course, I don't know the distribution so I have to estimate it from my sample.
The total amount of emissions measured is about 6500, and the measured time is 900 seconds. My first thought was, perhaps naively, that the sample mean using the maximum likelihood approach, would be 6500/900 $\approx$ 7. As mentioned in this post:
This sounds easy and comfortable and would mean that the standard deviation would be around 2.6. But it would also mean that the error bars would be of constant length, which I feel doesn't really make sense if I look at my graph, where the oscillations are much greater near the end of the graph. I feel that the error bars there should be larger. Am I wrong in this?
Any help is appreciated, thank you.
EDIT: Since I was unclear in the post, according to the instructions for the laboration exercise, I'm supposed to have error bars on the raw data. To quote the instructions: "Determine the statistical error for each data point and show the errors in the plot."
We are also supposed to give the statistical and systematic error for the half-lives themselves, but that's another thing.