I'm doing a compton scattering experiment, and I'm ahving trouble finding a good analytical way of determining where the peak is with its associated error. Its a counting experiment, so we use Poisson statistics, and we have the output of counts per channel over a range of 512 channels, each corresponding to an energy. There is a peak in the sprectrum of channels, and the counts in each channel have error of sqrt(counts). So I know the y-error bars for each channel and everything, and I can find where the half-max is on each side of the peak to get a fairly good idea of which channel the peak correcponds to, and we can eyeball the error in that value, but my question is, how can we do this more analytically? We know y-errors, and we want to translate that into an x-error of the peak basically. This seems so simple, but yet I'm having trouble establishing a method.