Appendix E 409 



ducts is then divided by n, just as in the long method. In find- 

 ing the mean a certain correction was applied to the guess. 

 Now, since we are here dealing with squares, we must apply as 

 a correction the square of the correction found previously ; but 

 unlike the previous procedure, this square of the correction is 

 always subtracted from the quotient found as stated above. 

 (All this has been proven mathematically correct, but the proof 

 is beyond the scope of this study.) The square root is then found 

 as before. The formula for deriving the standard deviation by 

 this method is : 



Using this method, we find the standard deviation to be 

 exactly the same as before, as shown in the table above and the 

 following calculations : 



<r ^A/ 1134QO -(- 1.56) 2 = 14.9789 cm. 



* OUL) 



A further considerable shortening of the short method can be 

 employed when the class values differ by amounts other than 

 unity or a simple multiple of it, such as 10. In such a case 

 the class differences are to be treated as unity and a correction 

 made at the end of the calculation. The modified formulas are : 



M= G (c x True Difference between Classes). 

 a- = -I/*' V-T) _ C 2 x True Difference. 



* 71 



The short method, because of its simplicity and its labor- 

 saving features, recommends itself for general use. It is also 

 slightly more accurate than the long method because no deci- 

 mals are dropped until the very end of the calculation. 



Coefficient of variability. Standard deviation, as a measure 



