436 TRANSMISSION 



this respect, and experience has shown that measurements can be 

 easily taken of sufficient accuracy to insure very reliable results. 



For obtaining the frequency distribution of a population with 

 respect to some measurable character, it is impracticable to lay 

 down specific rules in regard to the accuracy of measurements. 

 This must be settled largely by experience and common sense. 

 It may, however, be said here that in measuring a large popu- 

 lation, under the free action of the laws of probability, substan- 

 tially as many measurements will be taken too large as are 

 taken too small. Hence slight errors in measurements do not 

 appreciably disturb the mean and variability of the population, 

 because they tend to offset each other. 



Scheme of measurement. Reverting to the frequency dis- 

 tribution obtained from measurements of corn, it will be noted 

 that this population is distributed in classes or groups which 

 differ by a half inch in length. For the purpose of forming this 

 frequency table there would then be no object in taking the 

 measurements closer than the nearest half inch. This raises the 

 question of the inclusiveness of a class in grouping a population ; 

 that is, Should these measurements have been taken at the 

 quarter inch or perhaps at the even inch ? Here, again, no hard 

 and fast rule can be laid down ; but it may be said that in 

 general, and for the best results, the class range should be made 

 just large enough for some variates to appear in each class, 

 except, possibly, in a few near the extremes of the range of 

 variability when the total population is not very large. 



Sometimes the best unit for measurement and grouping 

 will be evident, but frequently some preliminary work is neces- 

 sary in order to decide it. For example, in beginning the 

 statistical work with corn we at first took measurements to the 

 quarter inch, with groupings accordingly, but found no results 

 different, either as to mean or variability, from those obtained 

 when measurements were taken to the half inch, and but slightly 

 different from those taken at the even inch. Accordingly we 

 are using the half-inch measurements for extreme accuracy and 

 the even inch for rougher work. 



Much judgment must be used in deciding upon the scheme 

 of measurements to be adopted and the groupings to be made. 



