460 Journal of the Department of Agriculture. — Nov., 1922. 



liushel of Wheat," by V. W. Peck, of the OfHre of Farm Manaye- 

 ment and ]']cononncs of the United States Depaitnieiit of Ag'ricul- 

 ture, may be quoted : — 



" What about the Average. 



" It is ({uite ])ossible, of course, to figure out the average cost of 

 a bushel of wheat for a given region — or for the whole country, or 

 even the world for that matter — provided the necessary data on cost 

 of seed and lal)our, use of land, etc., are available, but after such an 

 average is found it is a sort of statistical white elephant. The 

 average does not serve the purpose it is popularly supposed to serve 

 in establishing the right relation between costs and prices. 



" The average person— that elusive individual whom no one has 

 ever met, because, like the average cost of wheat, he is a mere 

 abstraction — may be evoked at this juncture to ask the natural 

 question : ' Why will it not do to use average as tlie measure of the 

 cost of i)roducing wheat? ' 



" Why the Average may be Misleadinc;. 



" 'J^lie answer to this (juestion nuiy be framed with an eye to 

 the fact that the public mind is prejudiced in favour of the average 

 as a statistical yard-stick, since it has been so largely used as such. 

 If the average cost were set up as a standard, we would have merely 

 a 50 per cent, standard, since the average tends to divide the figures 

 into two groups of about equal size, so that about half the farms 

 c(uicerned show u]) as producing wheat at a cost above the average 

 and half at a cost below the average. On this basis, if the average 

 cost should determine the price, about half the farmers would be 

 producing at a loss. When the price of a coinnuodity goes so low that 

 production is a fifty-fifty gamble, the tendency for many of the 

 producers is to quit and go on raising- some other crop that promises 

 a better chance of profit. The results may be under-production and 

 a period of higher prices." 



Fortunately it is possible to obtain by tlie use of certain formuhie, 

 figures which do convev an idea of the range of anv series and of the 



reliabilitv of the average. These formulae ai-e ().(i7 W " — r for the 



It - ] 



probable error and \ t- for the standard deviation. From these 



figures it is also possible to calculate by means of the formula /E," + E/ 

 the probable error or the reliability of the diflterence of two probable 

 errors ; and it is possible to ascertain the measure of certainty which may 

 be attached to any gx'oup of results. Without the use of these figures, 

 the interpretation of any set of results of agricultural experiment may be 

 erroneous and misleading. 



\' Ai;ii:i 'I Trials. 



Ill I liese (rials il is often necessary, owing to shortage of seed 

 or other circumstance, to plant a limited number of rows only. In 

 this case, the eit'ect of the lack of competition on the outside rows 

 must be g'uarded against. As an example, in six plots of maize, each 

 of four rows, at this institution recently, the average weight of grain 

 and straw obtained from the two inside rows was 1)8 lb. j)er plot, 



