UNKNOWN MEAN OF SAMPLED UNIVERSE 



643 



The four frequency distributions of h just considered are the same 

 as those shown in more detail in Fig. 3 ; the corresponding distributions 

 of the standard deviation are found detailed on Fig. 4. 



(d) If the interpreter of the data is closely familiar with the sampled 

 product and has been observing similar lots for some time he may 

 have a reasonably good idea as to the value of the general average 



1.0 

 0.9 

 0.8 

 0.7 

 0.6 



iiJO.5 



0,0.4 

 9- 



03 



02 



0.1 



01 2345678 



a = STANDARD DEVIATION 



Fie. 4 — Typical a priori frequency distributions of the standard deviation. 

 l—c = 3, a = C52 = 13.1922. 



II — c = i, a = 



III— c = 3, a 



1 - .15- 



= 23.5467. 

 = 9.1629. 



1 + .15 



IV— c = d, a = cs"- = 26.3845. 



of items produced under these same essential conditions. In Cases 

 Nos. 8 to 19, inclusive, use is made of this knowledge on the assumption 

 that X, the mean of the sample, turns out to be so nearly equal to M, 

 the most likely a priori value of the true mean m, that we may safely 

 call them identical. Three values of N, regulating the spread of the 

 Wi(m) distribution to conform to the observer's best judgment of 

 the true circumstances have been associated with the same sequence 

 of a priori assumptions regarding the precision constant as were 

 presented in Cases Nos. 3 to 7. 



