108 BINOMIAL AND NORMAL DISTRIBUTIONS Ch. 4 



normal-arithmetic graph paper appear to deviate only slightly from 

 a straight line. 



(c) The distribution of the farm acreages in Ness County, Kan- 

 sas, is essentially normal except that the lower end of the distri- 

 bution is missing, that is, the distribution is truncated. 



(d) The fictitious distribution of Table 4.53 clearly is not nor- 

 mal because the points of the r.c.f. graph definitely do not follow 

 a straight line on normal-arithmetic paper. 



It should be noted with respect to the conclusions above that only 

 gross (and hence certainly serious) non-normality will show up 

 under this sort of scrutiny. A look at the frequency distributions 

 associated with (6) and (c) above shows that there certainly is 

 some lack of normality. Figures 4.56 show this clearly ; but whether 

 or not the relative departure from a straight line is negligible will 

 depend on the particular circumstances. Discussion to be given 

 in Chapter 6 will be helpful in this decision. 



PROBLEMS 



1. Plot the following pairs of values of X and Y as points on a graph, using 

 semi-log paper with Y measured on the logarithmic scale. Then determine the 

 slope of the straight line through the points and relate it to the way Y changes 

 per unit increase in X. 



X: 1, 2, 3, 4, 5, 6. 

 Y: 2, 6, 18, 54, 162, 486. 



2. Plot Y\ = logio A" and Yi = 5 logio X on the same sheet of arithmetic graph 

 paper and also on the same sheet of semi-log paper. What effect does the coeffi- 

 cient 5 have on these graphs? 



j -cr-i)2 



3. Plot the r.c.f. curve for y = — y= e 50 on normal-arithmetic graph 

 paper. 5V2tt 



4. Plot the following tabular r.c.f. distribution on normal-arithmetic paper and 

 comment on any lack of normality revealed by your graph. 



5. Make an r.c.f. distribution for the fly counts of problem 1, section 2.4. 

 Plot this distribution on normal-arithmetic paper, and discuss any apparent 

 non-normality of this distribution. 



