320 ISOTOPIC TRACERS AND NUCLEAR RADIATIONS [Chap. 10 



M 



A.D. = 



\ \n— tii\ 

 t = i 1 



IfM»l, 



VM(M - 1) h \/^ 



M 



cpm 



A.D. = i= 



where 



M 



Xi = tii — n 



M 



cpm 



n = 



X ni 



M 



cpm 



and the vertical bars indicate absolute values. These formulas may be 

 applied when counting by predetermined time intervals /,-, or by predeter- 

 mined count number intervals «,-, or by arbitrary choice of both. 



10.14. Standard Deviation. The standard deviation a of a measurement 

 is defined as the root mean square of the deviations from the mean value of 

 the counting rate. 



M 



Y \n — ni\ 2 



t = l M-l c P m 



Also a more convenient iorm is generally used when a single measurement of 

 N total counts is taken over a time / 



4 



cr = \/nt = \/ r N counts 



which is the standard error in terms of numbers of counts. In terms of 

 percentage, 



100 



Vn 



% 



If several sets of measurements are taken, the resulting standard deviation is 

 then the square root of the sum of the squares of the separate o-'s 



M 

 2 — V ^2 



cr 



Either this method or the one above may be used for computing cr. The 

 error in any counting measurement must necessarily include the standard 



