Sec. 4.1 THE BINOMIAL FREQUENCY DISTRIBUTION 81 



constructions of these figures, using only the numerators of the terms 

 as explained above. 



The r.c.f. distribution for a binomial situation is discontinuous — 

 as is expected — and involves successive ordinates, each at least as 

 large as the preceding one to its left on the graph. Such a graph is 

 shown in Figure 4.13. If we were to draw a smooth curve through 

 the tops of the ordinates, it would have the same general appearance 

 as the r.c.f. curves drawn in Chapter 2. 



Fundamentally the frequency and r.c.f. tables corresponding to 

 Figures 4.11 and 4.13 are as shown in Table 4.11. The meaning and 



TABLE 4.11 



Frequency and r.c.f. Distributions for the Binomial Distribution 



Defined by p = q = 1/2, n = 10. Total Frequency Taken = 1024, the 



Sum of the Numerators of the Series for (1/2 + 1/2) 10 



S(/) = 1024 



use of Table 4.11 are fundamentally the same as for similar tables 

 in Chapter 2, but some differences should be noted. The major dif- 

 ference arises from the fact that the class "intervals" now are just 

 isolated points on a scale of measurement appropriate to r. For 

 example, 5% per cent (0.055) of the observed values of r (over a very 

 large number of observations on r) will be at or below r = 2. How- 

 ever, these observed numbers of occurrences of E will be 2's, l's, and 

 0's only: there is no such r as 1.6, for example. Another difference 

 between Table 4.11 and similar tables in Chapter 2 is that the former 

 is a theoretical table which fits any situation for which p = 1/2 and 

 n — 10. The frequency tables in Chapter 2 were relevant only to the 



