638 



-fRANSACT^lONS OP SECTION P< 



staudard deviation is given it is coneidered tliat the class is too small foi? ttny 

 good'lbrecast.' 



We are thus able to forecast that about 7 per cent, of the investments yield 

 nil, 27 per cent, between 31. and 4/., 29 per cent, between 4/. and 51., 15 per cent, 

 between 51. and 6/., and the remaining 20 per cent, yield over fl/. per 100/. 



While the above was in the press I tabulated the Whole group, and entered 

 the numbers in the column ' Actual Distribution ' in the proof. It is seen that the 

 agreement between prediction and fact is most satisfactory except in the case of 

 the group above 8/.^ 



The average yield calculated must not be confused with the average return to 

 capital invested; it is simply the average of the rates tabulated, taking all the 

 companies as of equal importance. 



The standard deviation is thus calculated : If m examples are found in 400 samples,, 

 the deduced frequency for the class is =p, with standard deviation for the 



percentage found in class approximately 100 • jPsJZSl, 



The numbers in the 2nd to the 5th columns belong, row by row, to normal 

 curves, witb the centre given in the 6th and twice the standard deviation given in 

 the 7th column. Thus, in the 3rd row, the average is 9|^, the standard deviation for 

 100 is 2 X 1-46 (1'46 being the deviation for the average of the four columns), and tlie 

 four cases (10, 10, 7, 9) are all within the standard deviation. 



^ Among the 3,878 cases there are 27 yielding exactly 10/. per cent.; of these 

 8 appeared in my sample of 400. There are in all 149 yielding from 8/. to 

 lOZ, 19«. ^d. ; of these 29 appeared in my sample. The chance that so many as 29' 

 should come in perfectly random sampling is only -0008, say the chance of drawing' 

 two named cards from a pack of 52. I cannot discover anything in my process to 

 lead to such a result 



