18 



THE MEASUREMENT OF VARIATION. 



cent, of all the observations fall below it in magnitude, 

 and 50 per cent, above it. The actual number of ob- 

 servations made is obviously represented by the area of 

 the figure enclosed by the curve and the abscissa line, 

 or the so-called " polygon of variation." The area to 

 the left of the median corresponds to the half of the 

 observations of less magnitude than the average, and 



SAQ, M Q 9 A'S' 



FIG. 4. Normal Curve of Error. 



that to the right, of those of greater magnitude. Now 

 let two other ordinates, Q l and Q 3 , be erected so as to 

 divide each of these areas into equal halves. We 

 now have four areas representing four numerically 

 equal groups; i. e., all the observations of small magni- 

 tude from to 25 per cent, of the whole; those of 

 greater magnitude, from 25 per cent, to 50 per cent, of 

 the whole ; those of greater magnitude than the average, 

 representing 50 per cent, to 75 per cent., and finally 

 those of greatest magnitude, representing the remain- 

 ing 25 per cent. Half of all the observations there- 

 fore exceed the limits of these ordinates Qj and Q 3 , and 

 half of them fall between or within them; so the dis- 

 tance on the abscissa line from M to Q, or M to Q 3 , is 



