QUANTITATIVE METHOD AND PRIMORDIA 29 



measured property is obtained, which may be represented by a 

 table of figures, or plotted out in the form of a diagram, in 

 which the intervals are represented by equal segments of a 

 horizontal line and the number of specimens in each interval 

 by the length of a corresponding vertical ordinate erected in the 

 middle of the interval. 



EXAMPLE: D. C. M'INTOSH has measured the disc- 

 breadth of 1000 specimens of Ophiocoma nigra.^ The following 

 curve was obtained (in millimetres) : — 



Disc-breadth 4 5 6 7 8 910 mm. 



Specimens 6 17 34 59 109 137 195 



Disc-breadth 11 12 13 14 15 16 17 mm. 



Specimens 174 141 90 26 9 i 2 



The arithmetical mean of all the measurements (10,106 mm. : 



1 r 



Fig, I. — Variation Curve of the Disc-Breadth of Ophiocoma Nigra. 

 14 Intervals 



1000) is 10 -I I mm. The most frequently occurring measure- 

 ment is one of 10 mm. 



We remark (i) that there is a heaping up of the measure- 

 ments (specimens) in the region of the mean value ; (2) that 

 measurements deviating from the mean (hump of the curve) 

 occur less and less frequently in a rough proportion to their 

 degree of deviation ; (3) that the measured property varies 

 between certain Hmits (4 and 17 mm.) ; (4) that the distribu- 

 tion of the measurements follows approximately the law of 

 frequency of error and is therefore ruled by chance (see § 108) ; 

 (5) that two factors are taken into account : the absolute value and 

 the frequency of each measurement. (Example : the frequency of 

 the specimens the disc-breadth of which is 7 mm. is 59 : 1000.) 



Using the method of which the above example gives some 



* D. C. M'INTOSH, "Variation in Ophiocoma Nigra," Biometrika, vol. ii. 

 (1902-1903), pp. 463-473- 



