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 



A=4X (Standard Deviation) 2 =4<7 2 . 



Example of Normal Curve. Number of rays in lower valve 

 of Pecten opercularis from Firth of Forth: 



V } F-Fo /(F-F ) /(F-F ) 2 /(F-F ) 3 /(F-F ) 4 



14 1-3-3 9 -27 81 



15 8 -2 -16 32 -64 128 



16 63 -1 -63 63 63 63 



17 154 



18 164 1 164 164 164 164 



19 96 2 192 384 768 1536 



20 20 3 60 180 540 1620 



21 2 4 8 32 128 512 



n = 508 342 864 1446 4104 



.4 = Fo+ vi = 17 +.6732 = 17. 6732. 



/ 2 = 1.7008 -0.7059 2 - 1.2475; <r=\///2=1.1169. 



// 3 = 2.8467 -3 X 0.7059 XI. 7008 +2 X0.7059 3 = 0.0217. 



/t 4 =8.0787 -4 X0.7059X2.8465+6X0.7059 2 X 1.7008-3X0.7059 4 =4.4223 



v 2 2 -2v 1 4 3( 1 .7008 ) 2 - 2 X -7_05_9 4 _ 

 v 4 8.0787 



Theoretical maximum frequency, 7/0 = -j= = 181.5. 



The probable discrepancy, based on the five larger values' 

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

 tablelike Table IV: 



