26 STATISTICAL METHODS. 



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

 imately the number of classes into which the magnitudes of 

 the variates should fall. If the standard deviation be known, 

 A may be found by the equation 



J=4X (Standard Deviation) 2 =4<r 2 . 



Example of Normal Curve. Number of rays in lower valve 

 of Pecten opercularis from Firth of Forth: 



V 



14 

 15 

 16 

 17 

 18 

 19 

 20 

 21 



= 508 



342 



864 



-27 



-64 



63 







164 

 768 

 540 

 128 



1446 



81 



128 



63 







164 



1S36 



1620 



512 



4104 



A = F + vi = 17 +.6732 = 17.6732. 



/m2= 1.7008 -0.67322 =1.2475; <r = V^ =1.1169. 



^ =2.8465 -3 X0.6732 Xl.7008 +2 X0.67323 =0.0217. 



/x 4 =8.0787 -4 X0.6732 X2.8465 +6X0.67322 Xl.7008 -3 X0.67324 



02172 4 4223 =4.4223. 



U.u^J.* r\ (\f\f\n. a -z.-m&'J QA~\ A 



2 ~ i 1 i 7To = ^.o414;. 



-0.00047 ; F/jL 2 3 = 0.0009. 



0.0002 X5.8414 2 



4XH.3650X(-0.3178) 

 3v> 2 -2v 1 4 _3(1.7008) 2 -2X.7059 4 _ 

 v 4 " L 8.0787 



508 



Theoretical maximum frequency, 2/0 = 



cV2 1.1169V2^ 



= 181.5. 



The probable discrepancy, based on the five larger values 

 of y, is found as follows, the Xi values being taken from a 

 tablelike Table IV: 



