Uncertainty of centroid and full-width at half maximum determinations and the effect of binning data

The uncertainties in determining the centroid and FWHM of Gaussian-shaped peaks by moments calculations and least squares fitting have been studied. The theoretical uncertainty for the moment calculation method has been derived and found to be the limiting uncertainty for both the moment calculation and least squares fitting. The results of the uncertainty studies have been used to assess the legitimacy of assuming that histogrammed data can be approximated by the continuous Gaussian shape. Increasing the number of bins in the peak was observed to improve the approximation of a continuous distribution. For example, FWHM⩾11 and FWHM⩾15 bins were necessary for the experimental standard deviation of the FWHM to be ⩽5% and ⩽1%, respectively, of the expected standard deviation for a peak with 10000 counts. Likewise, the uncertainty in determining the FWHM will be minimized under this criteria. The centroid uncertainty is not minimized under these conditions; however, this uncertainty is some fraction of a single bin and thus is relatively small