THE GRAPHIC PLOTTING OF DATA 



167 



scale of diameters, by inches, is then placed along the horizontal scale while the 

 volume scale is entered on the vertical scale. The whole forms a system of rectan- 

 gular co-ordinates. Each point on the paper represents two quantities, a diameter, 

 measured parallel with the base, and forming the abscissa of the point, and a 

 volume, measured vertically, and forming an ordinate. This is illustrated by 

 Fig. 26. 



In this figure, the volumes of three average trees, or the averages volimies of 

 three groups of trees have been plotted, namely, 10-inch, 13.15-inch and 16.1-inch 

 trees. The horizontal and vertical values of each point are indicated by dotted 

 lines. If the theoretical 

 relation of volume, and 

 diameter for all points 

 is as y to px~ we would 

 not only expect y (vol- 

 ume) to increase faster 

 than X (diameter), but 

 this increase would be 

 in the form of a regular 

 curve, and once the 

 position of this curve 

 is indicated by a suffi- 

 cient number of reli- 

 able points, all other 

 values for x and y, 

 representing the vol- 

 umes for all diameters, 

 would fall on the same 

 curve. False or ab- 

 normal average vol- 

 umes obtained from 

 too few trees will not 

 fall exactly on the 



curve, but above or below it. The greater the number of trees used in obtain- 

 ing an average point, the more closely will the point representing this value approach 

 or coincide with the curve. 



The actual shape of the curve will depend upon the relation arbitrarily estab- 

 lished between the two scales. Doubling the values on the ordinates, for instance, 

 reduces the ordinate distance one-half. The scale selected must bring all values 

 within the boimdaries of the sheet, which is usually accomplished if the largest 

 ordinate is not less than one-half nor greater than one and one-half times the 

 greatest abscissa. 



The value of using this method is that each separate point or average aids in 

 establishing the law, or fixing the values for all the others. If enough good or 

 well-weighted points are obtained, they correct the abnormality of other points 

 based on insufficient data and even show up arithmetical mistakes in obtaining 

 these averages. The curve makes possible the mterpretation of missing data, but 

 it is considered unsafe to extend it to cover values beyond the hmits of the original 

 data. 



Although from the standpoint of mathematics it makes no difference which 

 variable is plotted on the horizontal and which on the vertical scale, yet as the 

 purpose of this plotting is to convey to the eye the tendency or law of increase in 



10 11 12 13 

 Axis of Abscissae 



14 15 16 Inches of D.l 



Fig. 26. — Rectangular coordinates, showing position of 

 a curve of volume on diameter as determined by three 

 points whose ordinates and abscissae are known. 



