15.3 Try the above exercise, first taking the file saved in Exercise 15.2 and binning the data into a 40 bin histogram. Then use the χ2 method with a general minimizing program. Although some information is lost by binning, the fitting is often simpler and less time-consuming on the computer when the data are binned. Each evaluation of χ2 for this method involves evaluation of the density function only Nbin times not Nevent times as was the case for the maximum likelihood method. Your bins should be considerably narrower than the width  of the resonance if you wish to get accurate results. For this exercise, you may use the value of the density function at the center of the bin times the bin width rather than the exact integral over the bin. (As we indicated earlier, for careful work, you should not use this approximation.) Plot the data histogram and the fits from Exercise 15.2 and this exercise.