Sec. 2.4 FREQUENCY DISTRIBUTIONS 23 



9. Suppose that 5 bushels of the $3 peaches, 10 of the $2 peaches, and 15 

 bushels of the $4 peaches were purchased. What was the average price per 

 bushel ? 



2.4 FREQUENCY DISTRIBUTIONS 



To introduce the method of constructing frequency distributions, 

 and to show what sort of information can be derived from them, 

 reference is made to the numbers of Table 2.01. It is possible by 

 means of problem 11, section 2.1, to calculate that n = 95.7 and 

 a — 26.1. These statistical constants furnish some useful information 

 about the population of scores, but they fail quite badly to sum- 

 marize them adequately. For example, a person who made a score of 

 120 could not be told accurately how he compared with the others 

 taking this same test, and that information usually is important in 

 the use of such tests. One way to obtain this sort of information is to 

 construct frequency distributions and graphs which display the out- 

 standing features of the population. 



Two types of summaries of distributions will be considered both 

 numerically and graphically: a frequency and a relative cumulative 

 frequency (or r.c.j) distribution. Both distributions will be de- 

 scribed by means of a grouping of the individual scores into con- 

 venient score classes, even though such frequency distributions could 

 be made without grouping the members of the population into classes. 

 The scores then lose their individual identities and become members 

 of ten to twenty groups. The data become more manageable, and 

 little accuracy is lost in the process. To illustrate, consider Table 

 2.01 again. The extreme scores have been noted previously to be 23 

 and 183 so that the range is 160. If the range is divided by 10 a 

 quotient of 16 is obtained. Classes of that length would give the 

 minimum acceptable number of classes; hence for convenience in 

 tallying (as shown below) the class interval will be taken as 15. 

 Table 2.41 was constructed starting with the lowest score at 10 purely 

 because it was convenient and the lowest class included the lowest 

 ACE score in Table 2.01. The actual tallying of the data is shown, 

 as is the summarization of the tallies into a frequency (/) for each 

 class. In Table 2.42 a more concise form of the frequency distribu- 

 tion is shown along with the r.c.j. distribution. The latter distribu- 

 tion gives the decimal fraction of the ACE scores which were less 

 than or equal to the upper limit of the corresponding score class at 

 the left. For example, practically one-third (actually .332) of the 

 scores were at or below a score of 84, according to Table 2.42. 



