EMPIRICAL STUDIES OF MEASUREMENT 



percentile), is for a sampling of 100 or more of a series scored on_a 

 reasonably fine scale nearly as accurate as the measures that take 

 account of the amount of every deviation. The facts for my series 

 are given in Table II. In general the arguments that support the 

 median as a measure of central tendency, support also the Quartile 

 as a measure of variability in the case of large samplings from finely 

 scaled series (say of 100 or more cases of a series with 20 or more 

 steps). In the case of smaller samplings the calculation of Q. is 

 often as long as that of the A.D. 



If the report of an investigation gives somewhere the entire dis- 

 tributions the author may properly compute only the medians and 

 Q.'s. If the average is used as the measure of central tendency the 

 Q. is of course not very advantageous, since an approximate A.D. 

 will have been calculated in getting the average. 



Table III. gives the results of the individual sets drawn. It is 

 not necessary to examine it to follow the discussion past or to come, 

 but I insert it for the sake of any student who may wish to make 

 calculations from its facts other than those which I have made in 

 Table II. 



TABLE III. 

 SERIES A 



N. Av. M. 



101 100.2 99.8 



105 101.2 100.1 



101 100.0 99.3 



Sum of 



Dev. 1.4 1.0 



A.D. 

 10.0 

 10.6 

 10.4 



12.0 

 13.0 

 13.0 



9.3 



1.0 1.6 



N. 



101 



100 



100 



Sum of 

 Dev. 



Av. 

 .5 

 + 1.0 

 + .2 



1.7 



SEEIES B 



M. A.D. 

 1.0 6.6 

 + .4 6.3 

 0.0 5.9 



8.3 

 7.7 

 7.3 



Q. 

 5.2 

 5.6 

 5.4 



1.4 



.8 1.1 .4 



52 99.1 98.8 11.3 14.9 8.6 

 64 100.9 101.6 9.3 12.0 6.1 



50 .3 + .3 6.0 7.6 5.3 



51 2.4 2.5 7.9 9.7 6.6 

 50 + 1.7 + 1.6 5.7 7.4 4.1 

 50 + .6 + .2 5.1 6.7 3.8 



Sum of 



Dev. 



5.0 



4.6 3.5 2.6 4.2 



10 .8 + 1.0 5.0 5.7 4.3 



10 + .6 + .7 4.4 5.7 4.3 



10 3.2 2.0 6.2 8.3 4.8 



10 +1.6 +5.0 8.8 11.1 6.0 



10 2.8 2.0 7.0 8.3 5.5 



Sum of 



Dev. 9.0 10.7 6.4 7.5 3.5 



