4 EMPIRICAL STUDIES OF MEASUREMENT 



The results of these drawings are summarized in Table II. In 

 Table II., Nt = ihe number of sets drawn; A T c = the number of 

 cases in each set; Av.=the average divergence of the obtained 1 

 from the true 2 average; Med. = the average divergence of the ob- 

 tained from the true median; A.D. = the average divergence of 

 the obtained from the true average deviation; <r = the average 

 divergence of the obtained from the true mean square deviation; 

 Q. = the average divergence of the obtained from the true (75 per- 

 centile 25 percentile)/2. 



The figures for the last three divergences under 'Actual' are the 

 direct results; the figures under 'Percentile' are these divergences 

 in percents of the true fact. 



The table shows that there is not enough superiority in accuracy 

 in any case to outweigh the practical advantages which the median 

 has as a measure of such quantities as prevail in the mental sciences. 3 

 The divergences of the medians are on the whole only about 22 per 

 cent, greater than those of the averages, f^ 



TABLE II. 

 DIVERGENCE OF OBTAINED FROM TRUE 



ACTUAL PERCENTILE 



Nt Nc. Av. Med. A.D. <r Q. A.D. a Q. 



SERIES 

 A 



10 1.80 2.14 1.28 1.50 .70 2.06 1.92 1.30 



2 275 .045 .055 .05 .075 .055 .22 .26 .28 



3 110 .11 .17 .04 .04 .21 .17 .14 1.05 

 5 55 . .33 .43 .18 .18 .22 .78 .62 1.10 



25 11--' .62 .77 



,. 7 100 



.33 .53 .097 .081 .14 .31 .22 .48 



T.O .34 .59 .19 .16 .21 .61 .44 .71 



.86 1.04 



1 Obtained, that is, from the limited number of cases in the drawing in 

 question. 



2 ' True ' meaning here that obtainable if all the measures of the total 

 series are taken. 



8 The general merits of the median are not discussed in this report; so 

 also in the case of the general merits of the average deviation and of per- 

 centile measures of variability. To thoughtful students of mental measure- 

 ments they will be obvious. The matter is briefly discussed in my ' Mental 

 and Social Measurements' ('04) pp. 37 ff. and passim. 



