I am working to fit some data with a Gaussian model, the data comes from an experiment with a measurement error in the same order of the data points at the tails, both are in order $10^{-6}$, what I do is try to minimize $f$ where $$f=model-data.$$ My question is: Should I account for the measurement errors in the fitting? if yes, how can I modify $f$ to account for it?
** The peak value is in order $10^{-3}$, the data is a set of 20 points, where 3 points at each side of the tails have measurement errors in the same order as the data point itself.