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 trend as the number of telephones in use has increased, there is, after all, no real proof in the chart that the rates have decreased in proportion to the increase in the number of telephones in use. Fig. 116 stimulates interest and makes one wish to plot another chart in which the number of telephones in use would be the horizontal scale and the average rate paid would be the vertical scale, somewhat on the general scheme of Fig. 119. The plotted points for different years on a chart of the kind suggested would show by the arrangement of the points whether the prices had changed exactly in accordance with the number of telephones in use.

Courtesy of Data, Chicago

Fig. 116. Chicago Telephone Rates per Year Compared with the Number of Telephones in Use in Chicago

It is the object in this chart to show that the rates have been consistently reduced as the number of telephones has increased. The curves shown earlier in this chapter have varied directly, usually going up or down simultaneously. Here we have an inverse relation, with one curve coming down as the other goes up

Fig. 117 has been very carelessly drawn in that the two curves do not have their vertical scales start at the same zero line. The zeros for each of these scales are so close to the curves as drawn that it would have been a very simple matter to have made one zero line for both scales at the bottom line of the chart itself. The adverse criticisms of Fig. 114 may be applied to this chart also.

Though the two curves in Fig. 117 seem to show some inverse relation, since one curve frequently goes up when the other curve comes down, the chart does not permit any measurement by which the degree of correlation can be determined. The student who wishes to experiment with this interesting set of data would do well to make an entirely new chart with the two curves plotted from one zero line. After this first chart has been made, a second chart can be drawn in which the "Price" curve would be plotted exactly as in the first chart. The curve for the number of barrels of "Exports" should, however, be plotted downward from the top of the chart, after a good position has been selected for the top of the chart so that the "Exports" curve plotted downward from the top would coincide as nearly as possible with the "Price" curve plotted upward from the bottom. The scales for the