^HO COI.I.ECTTON f)F STATISTICS. 



of the area ; o^, the above equality- is not recjuiretl, in which 

 case anj' quaUty can be used as the standard, frequently 

 that being chosen, which exists over the greater part of the 

 area. 



Calriihdioii n-itJi ihc Mean (Jiialitii. — By mean quahty is 

 understood tliat. which, if it existed throughout the working 

 section, would produce the same total yield as that produced 

 by the several existing qualities in different parts of the 

 working section. 



Let «i, (t-2, (i;i ... be the several areas, 

 M .'/b !i2, .'Is • • • the corresponding annual yields, or 



increment, per unit of area, 

 ,, Y the mean yield per unit of area, then 



f'l X jfi + ((2 X ?/2 + ^'3 X //3 + • . • = (iiY -{- a.jY -\- ((3 r+ . . . 

 = Y {((1 + 02 + as. . .), 

 and 



y _ a I j/i -\- a2 i/2 + as P3+ ■ • • _ tot al annual yiel d 

 cii + «2 + 03 + . . . ~ total area 



Exitinplc : — 



A working section of 1,000 acres contains — 



Block (1) 200 acres with 60 cub. ft. average increment, 



„ (2) 100 ,, „ 50 ,, 

 „ (3) 200 „ „ 40 „ 

 ,, (4) 500 ,, ,, 80 ,, ,, ,, tlien— 



Menu quality 



^ 2 00 X 60 + 100 X 50 + 200 X 40 + 50 X 80 ^ ^^ ^^^^^ ^^ 

 ~ 1,000 



By reduced area is now understood that, which would 

 produce, with a uniform quality = Y, the same total yield as 

 the actually existing areas with their varying qualities. It is 

 obtained by applying, in each case, the inverse proportion of 

 that, which exists between the actual and the mean quality : 



}'; // =z (I : X and reduced area ./• = — =^' , 



