TYPE AND VARIABILITY 437 



If the unit of measurement be large, say two inches for corn, 

 the individual values will not be accurate ; the groups will be 

 large, but so far apart that the empirical mode will have but 

 little meaning. If, on the other hand, the units of measure be 

 too minute, say tenths of inches, the work of calculation will 

 be vastly increased, and while the empirical mode will be more 

 accurate, yet the distribution will not be " smooth," as the 

 technical phrase goes ; that is, some of the groups near the 

 extremes may not be filled. 



The scheme must be so chosen and the groupings so made as 

 to furnish a uniform distribution, with fairly smooth results 

 when the frequency is platted in the form of a curve. The 

 method of platting frequency distributions and dealing with 

 them as " curves of frequency " will be shown in the Appendix. 1 



SECTION IV PROBABLE ERROR 



Mention has already been made of certain inaccuracies in 

 measurements and groupings of a population. Attention is now 

 called to another source of error which arises from using a 

 limited number to represent the total population. From all 

 these sources slight errors are inevitable. We have no means of 

 determining the exact error, but after the work has been done we 

 may find a measure of accuracy. This measure of accuracy is 

 called the " probable error." 



Whatever the source of error, the exact discrepancy in a 

 result which depends upon measurements can never be ascer- 

 tained. However, the so-called " probable error" does give a 

 measure of accuracy which indicates whether we should expect 

 a large or small error in a determined value. In other words, it 

 indicates the degree of confidence which we should place in 

 results obtained by statistical methods. 



1 In general this may be done by laying off the measurements, as inches, half 

 inches, pounds, etc., on a horizontal line, and the numbers of individuals in the 

 distribution as verticals, connecting the points by a continuous curve. As num- 

 bers differ greatly in different cases, it is best to reduce them all to the basis of 

 100, and express all values in percentages. If this is done, then all curves of the 

 same measurement are comparable. 



