462 TRANSMISSION 



The value of r is found by means of the formula 



Systematic arrangement of work. The whole process, which 

 seems somewhat complicated, is after all quite simple. To 

 recapitulate, it amounts to multiplying the figures in each square 

 by both their own deviations (that is, by their deviation as to 

 length and their deviation as to weight), and then adding all the 

 results and dividing by the whole number (of ears) multiplied 

 by the product of the two standard deviations. (See formula 



r = ~^~^ JK ') In performing the actual work, however, it is 



highly important to have a systematic scheme for carrying out 

 the computations in order to avoid confusion in the somewhat 

 complicated details. It has seemed desirable, therefore, to 

 present the matter in the form of a detailed description of the 

 various steps involved. 



First step. Having given the correlation table of the popula- 

 tion, we first add the frequencies in the arrays with respect to 

 both characters ; that is, add the numbers in columns and rows 

 of the table. This gives two frequency distributions of the total 

 population, the one with respect to length of ears (/,), and the 

 other with respect to weight of ears (/^). 



The one with respect to length has the frequencies 4, 5, 14, 

 16, 19, 53, 64, 70, 75, 98, 114, 134, 142, 100, 53, 26, 5, i. 



The one with respect to weight has the frequencies 4, 22, 27, 

 50, 47, 71, 75, 71, 75, 88, 107, 114, 112, 65, 37, 8, 13, 4, 2, i. 



Second step. For each of these frequency distributions 

 (column f L and row /,) the means and the standard deviations 

 must be calculated. The method of making these calculations 

 is the same as the one used for mean and standard deviations 

 in general. It has already been fully explained, and therefore 

 need not be repeated here. A systematic arrangement of the 

 work is shown in connection with the table. The results are : 



mean length = M, = 7.85 

 standard deviation in length = o- 7 1.57 



mean weight = M lt - = 10.65 

 standard deviation in weight = a-,,. = 3.63, f' 



