An Apple Orchard Survey of Ontario County 211 



3d, the variability of individuals within the group; 

 4th, mathematical accuracy in tabulation. 



Accuracy of data. — One must not expect absolute scientific accuracy 

 in the figures of an orchard survey, for the following reasons: The data 

 are collected under varying conditions. Personal opinion plays an im- 

 portant role. One's judgment concerning conditions varies from time 

 to time. Many figures are doubtless an approximation. On the other 

 hand, many of the figures for yield and income recorded in the survey 

 were taken directly from the growers' books. These are of more value 

 than the approximations, and might therefore have been weighted. None 

 of the figures in the survey, however, have been weighted technically. 

 In spite of the chances for inaccuracy in the field reports, the law of proba- 

 bility of error is such that if the number of reports is sufficiently large, the 

 sum of the positive errors equals the sum of the negative errors and the 

 average will be reliable. 



Number of observations. — The weight to be given a series of observa- 

 tions is proportional to the square root of the series. A series of 400 

 observations should carry twice as much weight as a series of 100 obser- 

 vations. The numbers in the present survey are in many cases too small 

 to be of much value statistically. In all cases the average given would 

 be of greater value if based on far larger numbers, yet they form an in- 

 teresting indication of the probability of similar results being obtained 

 under similar conditions. 



Variability oj individuals within the group. — The number of cases 

 necessary to give weight to the result depends also upon the variability 

 of the individuals within the group. If the standard deviation is small, 

 there is little variation in the individuals. A much smaller sample, in 

 this instance, would represent the total population than in cases of great 

 variability. If the standard deviation is large, we should not expect to 

 find the mass of the individuals near the mean. 



Mathematical accuracy in tabtdation. — Not only is it necessary that the 

 field data should be as accurate as possible, but these figures must be tabu- 

 lated with mathematical accuracy. In tabulating the data, no effort has 

 been spared to make the lists accurate. In all cases the observed totals 

 as reported in the survey sheets were used in determining the average 

 yield and income per acre. When the yield was reported in bushels 

 the number was changed to the equivalent in barrels by dividing it by 3 . 

 In order that there should be no errors in addition, the lists for determining 

 the means were added on a Burroughs adding machine and carefully 

 checked. The averages in the tables based on the orchards of Group I, 

 in nearly all cases, were determined both by slide rule and by the ordinary 

 method, one serving as a check to the other. The averages for the tables 



