90 BELL SYSTEM TECHNICAL JOURNAL 



as has been utilized in developing the study. In many instances, 

 however, it is necessary to know not only the average value but also 

 the distribution of items about that average. 



Thus, the normal curves of the type of those shown in Fig. 4 

 serve as a basis for estimating the average message use of all 

 subscribers to a given class of measured service in a given city. 

 Additional curves are, however, required for estimating the dis- 

 tribution of subscribers by message use. 



The basic principles governing the derivation of normal curves are 

 the same whether these normals be concerned with averages or with 

 distributions. The detailed methods involved are, however, quite 

 different because of the inherent differences in the material. An 

 average can be expressed in one arithmetic term which, can be plotted 

 against other factors. A distribution, on the other hand, is a com- 

 plex entity which may itself be expressed as a curve but which obvi- 

 ously cannot be measured by an index to be plotted against other 

 variables without losing sight of certain detailed characteristics of 

 the distributions. The procedure and methods described above for 

 deriving normal curves are modified somewhat in the derivation of 

 normal distribution curves. Some of the methods which have been 

 found advantageous for these analyses are described below. 



The first step in the analysis is usually to plot the actual detail and 

 cumulative distributions for each group of items and to compare the 

 various distributions in order to determine points of similarity or 

 difference. For purposes of comparison, percentage distributions are 

 used, i.e., the per cent, of total items rather than the actual number 

 occurring in each interval is plotted. With homogeneous material it 

 will usually be found that when plotted to the same scales the detail 

 frequency curves are all of the same general shape but differ in three 

 primary characteristics. 



1. The spread or extent of variation. 



2. The location of the peak or point of maximum frequency. 



3. The concentration of items in the peak interval. 



These characteristics are, however, interrelated and to a certain extent 

 related to the average. 7 Other things being equal, it might be ex- 

 pected that: 



1. The greater the average the greater the spread. 



2. The greater the spread the less the concentration at the peak. 



3. The higher the peak the nearer it will fall to the average. 



7 Throughout this section the term "average" is used in the sense of arithmetic mean. 



