There were naturally fewer observations at either end of the chart, for the very small spans and for the very large spans, than for the intermediate spans. It was probably because of the small number of observations at either end of the curve that the dots there are so far away from the curve line. If more numerous observations were taken it is probable that all the averages would fall more closely on the curve line than seen in Fig. 164.

The ordinary course of procedure in making a correlation chart is to plot all the observations by the method seen in Fig. 163. Sometimes, however, the observations are so many as to make an extremely confusing chart if the observations are shown in the form of separate dots. In Fig. 164 the observations in any 1-inch class have been averaged and all the observations in one class are represented by a single dot. In Fig. 165 the dots would be very numerous, so numerous as to make it not feasible to show them on a small size chart. For Fig. 165 it was desired to show the maximum income and the minimum income, as well as the average income. Instead of showing all the dots on the chart, cross-hatching was used to represent the area in

GRAPHIC METHODS

whicli the dots fell. The upper edge of the cross-hatching shows the maximum of the incomes, and the lower limit of the cross-hatching shows the minimum of the incomes reported for different years after graduation. The reader can thus get the whole story at a glance without being confused by the complexity which would result if all the dots were shown. Attention should be called to the fact that the curve of average income falls much