Where to stick your data points: The treatment of measurements within wide bins

When a data point, measured over a bin of finite width, is to be compared to theoretical or model frequency distributions, neither the central value of the bin nor the weighted mean value (the barycentre) of the abscissa within the bin is the appropriate place to plot the data point. It is shown that such data points ought to appear where the value of the predicted function is equal to its mean value over the wide bin. Some consequences of commonly used but incorrect alternative data presentation methods in particle physics are discussed.