16 USE OF GRAPHIC METHODS 



the general aim should he io choose such unils (hot (lie curve loill 

 be neither very Jlat nor very sleep. This aim is (icconiplished if 

 the largest ordinate is not more than one and one- half times the 

 largest abscissa. Remember this in connection with all curves. 



3. Having determined the units for ordinates and abscissae, starting 



from the lower left-hand corner of the page lay off and mark 

 the respective values on each axis. Always label these carefully 

 along the edge of the paper; i.e., "Diameters in Inches," 

 "Heights in Feet," etc. 



4. In plotting the values remember, as before stated, that the hori- 



zontal distances from the vertical axis represent the values of 

 the abscisstr. (diameter values in this case), and that the ver- 

 tical distances from the horizontal axis represent the ordinates 

 (heights in this case.) 



The two variable quantities, the height for a specified diam- 

 eter, can be expressed by a single point on the co-ordinate paper ; 

 namely, that point at which the perpendicular lines extending 

 from the respective abscissa and ordinate axes cross. After 

 the location of the first point has been determined plot the 

 values of all other trees in the data supplied. Where a second 

 point occurs at the intersection of the same lines place a small 

 figure "2" beside the point already plotted, for a third point 

 of the same value a small figure "3," and so on. 



(6) Averaging the Values. 



5. When plotting is completed, the next step is to average the values 



in accordance with the object sought. In this problem the 

 average height will be determined for each 2-inch diameter 

 class in even inches. Remember that in all of these problems 

 two sets of averages must be obtained. In this problem we 

 have (1) the average heights for the diameter classes and (2) 

 the average diameter of each diameter class. Let each of the 

 diameter classes begin with the fractional part of the preceding 

 whole odd inch and end with the next succeeding whole odd inch, 

 of the diameter class, i.e., 5.1 inches to 7.0 inches inclusive will 

 comprise the 6-inch class. In 1-inch classes it should be from 

 5.6 inches to 6.5 inches inclusive. The average abscissa for each 

 diameter class will be found by adding horizontally the values of 

 all points plotted within each diameter class, and dividing by the 

 total number of points. Similarly the average ordinate for each 

 diameter class will be found by adding vertically the values of the 

 same points, and dividing by the number of points. With these 

 two average values at hand now plot the average point in its 

 proper place as was done with the points for the individual trees. 

 In order that this point may be distinguished from the others 



