Appendix E 411 



less than 37.94 - .4518 = 37.4882 cm., but would fall some- 

 where in between these two limiting values. It is symbolized 

 by E with the initial of the constant to which it belongs attached 

 in smaller case type. Thus, the symbol for the probable error 

 of the standard deviation is E ff ; of the mean, E M ; of the co- 

 efficient of variability, E G . 



The probable errors are based upon certain relations between 

 the standard deviation and the number of individuals. The 

 greater the number of individuals, the smaller will be the prob- 

 able error. In short, the probable error will indicate how much 

 confidence we can place in our constant, and should always 

 accompany the latter. It is really a part of the constant. 



In finding the probable errors the constant .6745 is used. 

 This has been derived mathematically and is used by all biom- 

 etricians in the same way. 



The following formulae will show how the various probable 

 errors can be found : 



#* = .6745-^ 



Vra 



E v = .6745?=. 



E = 



C 

 .6745 =, where C is 10 % or 



V2n 



.6745 =A/1 +2( \ where C is greater than 10%. 1 

 2i 71 \Hj{j/ 



Our completed constants for length of bean plants are then 

 as follows : 



M = 37.9400 .4518 cm. 



o- = 14.9789 .3195 cm. 

 (7 = 39.48 .96%. 



1 In these equations the value of C in per cent is to be used. The prob- 

 able error will come out as a percentage. 



