106 STATISTICAL METHODS. 



j . 



In the example, the data of which are given on p. 26, the 

 frequency between the limits is given in % column. The of 



G 



each limit (as an inner class limit) is found and the entries 

 in Table IV corresponding to the limits are taken. Each 

 such entry is subtracted from 0.50000, *Js multiplied by 

 100, and from the product is subtracted the total theoretical 

 percentage of variates lying between the outer limit of the 

 class and the corresponding extremity of the half curve. 

 This gives the theoretical frequency of the class in question. 

 The closeness of agreement of the last column with the 

 "Percent." column indicates the closeness of the observed 

 frequency to the theoretical. 



V. Table of log T functions of p. This table 

 will enable one to solve the equations for y Q given on page 32. 

 The table gives the logarithms of the values of F functions 

 only within the range p 1 to 2. As all values of the func- 

 tion within these limits are less than 1, the mantissa of the 

 logarithms is 1; but it is given in the table as 10 1 = 9, 

 as is usually done in logarithmic tables. 



Supposing the quantity of which we wish to find the value 

 reduced to the form r(4.273). The value cannot be found 

 directly because the value of p is larger than the numbers in 

 the table (1 to 2). The solution is made by aid of the equation 

 r(p + l)=pF(p), thus: 



log r(1.273) = 9.955185 

 log 1.273 =0.104828 



log T(3.273) = 0.060013 

 log 2.273 =0.356599 



log r(3.273) = 0.416612 

 log 3.273 =0.514946 



log T(4. 273) = 0.931558 



or, more briefly, log r(1.273) = 9.955185 

 log 1.273 = .104828 

 log 2.273 = .356599 

 log 3.273 = .514946 



log T(4.273) = 0.931558 = log 8.542 



