408 Plant-Breeding 



M= 39.5- 1.56 - 37.94cm. 



= - - 2.4336 = V 224.3664 = 14.9789 cm. 



500 



39.48%. 



In our problem, the mean as determined by this method, as 

 shown in the accompanying table, is exactly the same as was 

 found by the long method, 37.94 cm. 



We would have secured the same result if, after a casual in- 

 spection of the line of bean plants spoken of above, we guessed 

 that the mean was 39.5, and taking an individual of this length 

 as a measure, we found the total amount which the short ones 

 lack of being equal in length to the assumed mean, or the guess, 

 and likewise the total amount which the long ones exceed the 

 guess. The algebraic sum of these two amounts would be the 

 total amount by which our guess missed of being the true mean, 

 and since 500 individuals were measured, the average amount 

 by which we missed on each individual would be found by 

 dividing this sum by 500. Our assumed length would then 

 be corrected by this amount, just as above. If we had guessed 

 that the mean was 37.94, and went through the same process, 

 then the sum of the negative differences would have exactly 

 counterbalanced the sum of the positive differences, since our 

 guess in this case coincides with the true mean. 



It would have made no difference whatever had we made our 

 guess at 9.5. Indeed, this would have the advantage that 

 minus signs would be eliminated and thus a frequent source of 

 error removed, since students are prone to forget the algebraic 

 signs. On the other hand, larger numbers would be involved. 



In finding the standard deviation by the short method, the 

 elements of the (V-G) column are squared before multiplying 

 by the corresponding class frequencies. The sum of these prod- 



