20 STATISTICAL METHODS. 



(B) Subtract in order each theoretical value of y from the 

 corresponding observed value, regarding signs. Call the dif- 

 ference Si. Whenever in the successive values of 61 there is 

 a change of sign, divide the product of these successive values 

 of di, in pairs, by their sum. Call this value & 2 ; make its 

 sign always minus. Then the difference between the two 

 polygons in per cent of one of them is given by the equation 



^ 1 + ( _a,) 



3 



where 1 is summated without regard to sign, and n equals 

 the total number of variates. This is the method of Duncker, 

 '98. It may be considered a sufficient agreement between 



observation and calculation when A < -%. 



\'n 



THE NORMAL CURVE OF FREQUENCY AS A BINOMIAL 

 CURVE. 



The normal curve may also be expressed by the binomial 

 formula (p + <?)*, where p = \,q = -|, and I is the number 

 of terms, less 1, in the expansion of the binomial ; hence 

 approximately the number of classes into which the magni- 

 tudes of the variates should fall. If the standard deviation be 

 known, I may be found by the equation 



I = 4 X (Standard Deviation) 2 = 4cr*. 



Example of (nearly) normal curve. Number of spines in 

 dorsal fin of Acerina cernua, L. (Duncker, '99, p. 177). 



1900 298 740 382 1076 



M= Vm + v l = 14 + 0.1568 = 14.1568. 

 /*, = 0.3895 - 0.1568* = 0.3650. 



/m 3 = 0.2011 - 3 X 0.1568 X 0.3895 -f 2 X 0.15683 = 0.0257. 



