10 SUMMARIZATION OF DATA Ch. 2 



data as clearly and as concisely as is possible. A statistical descrip- 

 tion of a population will be found to be important also when the 

 population is to be studied by means of samples rather than in its 

 entirety. There are various widely used methods of accomplishing 

 such a purpose. The choice of a method depends upon what is to be 

 learned from the data, and upon the statistical characteristics of the 

 population which is being summarized. 



The need for statistical descriptions and summaries is pointed out 

 rather specifically by means of the data in Table 2.01. It contains 

 the 1290 ACE scores made by students entering Kansas State College 

 for the first time in 1947. An ACE score is intended to measure 

 certain features of a student's intellect and aptitudes which are 

 thought to be related to his success in pursuing one of the various 

 possible college curricula. If so, ACE scores should help the student 

 and the staff to do a better job of fitting the students' abilities and 

 interests to the facilities which the college has to offer. 



The reader is already generally familiar with the term average as 

 some kind of usefully typical number which partially replaces a 

 whole group of numbers; but he may be less familiar with the fact 

 that there are several averages in use. It should be intuitively 

 obvious that no single number, like an average, can be expected to 

 summarize adequately the set of data in Table 2.01. Some measure 

 of the variability exhibited by these ACE scores is needed; that is, 

 an adequate description of the way these scores are dispersed, or 

 distributed, between the lowest and highest scores is needed in addi- 

 tion to a description of the general level of performance. More 

 specifically, we need a standard method of describing any particular 

 student's score relative to the whole group of scores. With such in- 

 formation at hand, a trained adviser may be able to give a student 

 considerable assistance in the choice of a vocation or a profession, 

 or in the solution of personal problems. 



The statistical procedures described and illustrated in this chapter 

 will make it possible to replace the 1290 ACE scores by relatively 

 few statistical constants, graphs, and tables which still contain all 

 the really pertinent information embodied in the original popula- 

 tion of numerical measurements. Some of these possible procedures 

 will be introduced by means of small sets of data for the sake of 

 convenience. Thereafter, reference again will be made to Table 2.01. 



