36 STATISTICAL METHODS. 



*a= 18.0448 - 3.7965 = 14.2483 ; 

 3.7965X17.9857 



. ,__.., 

 =3.78401; 



14.24317.98 



18:0448 



14.2483X17.9857 

 18.0448 



2000 (18.9846)^17.9846 __.0833(. 0556 -.2643 -.0704) 



4/0 - 10 f\ A A O / _ A ^.1 JO'SO 



18.0448 V27rX 3.7840 X 14.2006 



=475.24, the frequency of the modal class. 



Position of the mode, y Q =A -D= 3.501 -.523 = 2.978. The close- 

 ness of fit to the theoretical curve is calculated below by Pearson's 

 method (page 24). 



F / Theoretical (y) d d* 



-1 0.0 0.0 



15 21.1 - 6.1 37.21 1.76 



1 209 185.8 +23.2 538.24 2.90 



2 365 395.1 -30.1 906.01 2.30 



3 482 475.2 + 6.8 46.24 .10 



4 414 405.6 + 8.4 70.56 .17 



5 277 272.1 + 4.9 24.01 .09 



6 134 147.6 -13.6 184.96 1.25 



7 72 65.9 + 6.1 37.21 .57 



8 22 24.1 - 2.1 4.41 .18 



9 8 7.0 + 1.0 1.00 .14 



10 2 1.6 + 0.4 .16 .10 



11 0.2 - 0.2 .04 



12 0.0 



That is, the probability is that in one out of every two random series 

 belonging to Type I we should expect a fit not essentially closer 

 than that given by our series, which, of course, assures us that this 

 distribution is properly classified under Type I. 



THE USE OF LOGARITHMS IN CURVE-FITTING. 



Most of the statistical operations can be greatly facilitated 

 by the use of logarithms. In curve-fitting their use becomes 



