230 



Bulletin 397 



then divided into two classes of equal production, their limits being from 

 3200 to 3249 pounds and from 3250 to 3299 pounds, respectively. The 

 same groups were next divided into four classes of equal production, the 

 Hmits of which were from 3200 to 3224 pounds, from 3225 to 3249 pounds, 

 from 3250 to 3274 pounds, and from 3275 to 3299 pounds, respectively. 

 Finally the groups were divided so as to have a lo-pound range, as from 

 3200 to 3209 pounds, from 3210 to 3219 pounds, and so on. The results 

 of this study are shown in table 6: 



TABLE 6. Effect on Variability of Changes in Range of Groups 



Group production, two-weeks period 

 (pounds) 



Range 



allowed 

 by group 



limits 

 (pounds) 



Number 



of 

 groups 



Coeflficient 



of 

 variability 



3,200-3,299 



3,200-3,249 

 3,250-3,299 



3,200-3,224 

 3,225-3,249 

 3,250-3,274 



3,200-3,209 

 3,210-3,219 

 3,240-3,249 



100 



50 



25 



10 



33 

 33 



31 

 20 



5 . 09 ± o . 42 

 503 ± 0.42 



4.88 ±0.43 

 4.60 ± 0.52 



The coefficients in table 6 decrease slightly as the group limits are 

 narrowed. The consistency of the results suggests the probability that 

 the narrowing of the limits is responsible for the decrease. However, 

 the difference between the highest and the lowest limits is not so great 

 as its probable error, and therefore no significance can be attached to it. 

 It would appear that if there is any decrease in variability caused by 

 lowering the range allowed by the limit below 100 pounds, it is so slight 

 that there is no object in using the narrower limits. 



Size of group as affecting variability. — It has been stated that group 

 variability decreases according to the square root of the number of indi- 

 viduals in the group. A short study was made of groups of different 

 sizes, merely to compare the observed values with the calculated values 

 and thus check the accuracy of the methods used. The values calcu- 

 lated for groups of different sizes from the figure for indi\-idual variation, 

 as found in table i, were compared with the observ^ed values for groups 

 of three different sizes. The results are shown in table 7 : 



.3-P 



