I have preformed the muon lifetime experiment at my uni's lab, and got the data. It's text file with 8190 numbers. My TDC unit was set so that the time gates were at 10 $\mu s$, and it has 8192 channels (first and last contained some kind of noise so they were not included in data analysis).
Now, I made a program in python that will sum every n data, and make a new list that I can then plot in bar plots and from that calculate the mean muon lifetime, because it decays by exponential law.
I also found that I can estimate the muon lifetime by using this formula:
where $N_i$ is the number of counts in the bin, $t_i$ is the 'time bin', and the bins go from $n_l$ (lower) to the $n_u$ (upper) bin.
Using that as a guide, I found that for my data I get the best estimate if I set the bin count at 7 (7 bins), and if I put 10, I get higher result. Now if I set the bin number to 20, I get even higher number.
But that sounds wrong. I mean, there must be some kind of catch. If I divide the time I get for 20 bins by two I get the correct result (~2.5 $\mu s$).
The pictures are like this:
So what am I doing wrong with interpreting this?