Mathematica (I use 10.1) has a function FindPeaks that should provide good starting values for mu`

nlm = NonlinearModelFit[data, 
  A 1/(\[Sigma] Sqrt[2. \[Pi]])
    Exp[-(1./2.) ((x - \[Mu])/\[Sigma])^2], {{\[Sigma], 100.}, {\[Mu],
     FindPeaks[data, 80., 0.2, 5000.][[1, 1]]}, {A, 200}}, x]

1st line should read: ... part of the problem is that your data are NOT very well described by a single gaussian

Thanks a lot!

I was not aware that I can set start values. This information is very helpful :-)

How do the start values influence the approximated values by mathematica? I have about 30 of these datasets where I do not expect sigma to change much but mu varies a lot. The point is, I want my notebook to evaluate the data automatically and I have set up everything to this point in that way. I have a formula to predict where mu should be, but if the start value affects the outcome of mu I'd rather use a different way.