\ \ XI-* LI" 6 ] 



cl\i\ 



we have to interpolate between ih. values of = 1"<) , , ,, sending to 

 2 log 2, ami // = 200, corresponding to :{ log 2; or, UHO the above formula (xxix) for 

 A- =2-078,072, when- y lt y n correspond to 50 and 100, and y 3 , y 4 to 200 and -MX). 

 \\V (dare here the values found I ron i the formulae for the moments and from Table* 

 X XXP XXXP by interpolation for p = '8, n = Ki 



By Moment Formula.- 

 M' an r -799088 



Mode- f -8045 



s.ix <r -028808 



By Logarithmic InterpoUtion 

 '799094 



-8045 

 -0288 Hi 



& '1478 -14<J7 



/3 2 3-2563 3-2555 



The diagram below shows the Pearson curve* 



y = 348586 x 10 u (a;- 599,6564) 5 *- 822 - 327 a;- 23!i - 282 ' 127 



computed from the interpolated constants, as against the ordinates found from 

 Table XXXIII. See p. clxiii above. 



DISTRIBUTION OF P IN SAMPLES OF 16O WITH PARENT POPULATION (J - H 

 14.00O 



COMPARISON OF PEARSON CURVE 

 ( TYPE XI ) FROM INTERPOLATED 

 CONSTANTS WITH COPIPUTID 

 ORDINATES AND NORMAL CURVE 



75 SO 



VALUE OF r IN THE SAMPLE. 



Pearson Curve 

 Normal Curve 



Computed Points o o o o 



It will be seen that the curve differs very considerably from normality, and agrees 

 closely with the exact points. 



Besides the constants of the r-frequency curve discussed in the last section, there 

 are several others that require consideration. These are in particular the position 

 of the mode r and the "most likely" value of p in the sampled population for a given 

 value of r in the single sample, this we will denote by p. We shall have further to 

 introduce a value of /o = /3, which we will term the "most reasonable" value. 



* Mean at -787,289, Mode at -781,827 from origin of curve. 



a II. 



