clii Tables for Statisticians and Biometricians [XXVII XXX 



The frequency curve for cr ai is given by 



The mean value a ai = ^ ^ ~^" _ ^' S t VI - p 2 (xxx). 



The modal value <r ai = */ - 2i Vl p 2 (xxxi). 



' 71 



The standard deviation 



When a sample is large, the above values reduce to : 



j 

 and o- = -- ^ 



Ul V2 



Table XXIX provides the ratio of the mean standard deviation of arrays in samples 

 a ai to the array standard deviation in the sampled population 2^ = 2 X VI p 2 . 



Table XXX provides the ratio of the standard deviation of the array standard 

 deviations in samples to the value of standard deviation of arrays in the sampled, 

 or parent population, divided by \/2?i, or the ratio 



It will be seen that even for relatively small samples, such as 15, this ratio 

 approaches within 1 / o of unity. On the other hand the ratio a a J^ Al fails to be 

 within 1 / of unity even for samples of 100. 



10. Distribution of Mean Value of y for a given x as found from the Regression 

 Lines of the Samples. 



Lastly we may consider what is the accuracy with which the mean value of the 

 variate y for a given value of the variate x can be determined from the regression 

 line of the sample. This line may be represented by 



& + ;(-*) ........................... (xxxiii). 



Thus y x depends on all the five quantities x, y, o- iy <r 2 and r as found from the 



v 

 sample. Now the mean value of y x is m z + p ^ (x m-^) and we will denote by y x 



2<i 

 the value of y x as measured from its mean, i.e. 



y = fix - m 2 - p ^ (x - Wi). 



' 



