6 HISTORY AND INTRODUCTION Ch. 1 



However, it is more commonly true that it is impossible, or un- 

 wise, to collect a whole population of numerical measurements. In 

 that event we obtain but a portion of a population for actual analysis, 

 and attempt to draw from it useful conclusions about the popula- 

 tion which was merely sampled. If the sample is to be useful it must 

 be adequately representative of the population; that is, it should 

 faithfully reflect the important features of the population. 



In the event that the whole population of data is available for 

 analysis, the purpose of statistical analysis is to reduce what is a 

 relatively large bulk of numbers to a comprehensible form by means 

 of graphs and tables and/or by calculating a few figures which con- 

 tain most of the important information theoretically available in the 

 original mass of data. For example, the ACE scores at the beginning 

 of Chapter 2 are numerical measurements which the college took in 

 the belief that they would be of value to the student and to the 

 school, perhaps by helping to determine what profession the student 

 should prepare to enter. Obviously those data are so bulky that they 

 demand some sort of condensation. 



It is worth noting at this point that even though the necessity to 

 analyze whole populations of data is a rare circumstance, it is not 

 logical to study the statistical analysis of samples without some ade- 

 quate knowledge of the statistical features of the populations from 

 which the samples are taken. Fortunately a considerable amount of 

 useful statistical analysis can be learned and appreciated without 

 studying more than two general types of populations. 



Whenever we attempt to base conclusions concerning a statistical 

 population of numerical measurements upon relatively few observa- 

 tions (a sample) from that population, we face two important gen- 

 eral questions, (a) How shall the sample be taken so as to maxi- 

 mize its chance of being representative of that population? (b) 

 Having obtained some numerical observations from the population 

 with question a in mind, how do we draw valid conclusions from the 

 sample? As an illustration, consider the following sampling prob- 

 lem. Suppose that a highway commission is considering the pur- 

 chase of some cement for highway construction, and that two com- 

 panies are offering their products for purchase. The commission 

 wishes to compare the seven-day tensile strengths of the two cements 

 before letting the contract. Obviously they must resort to sampling 

 because they can test only a tiny portion of each company's total 

 output of a particular sort of cement. It will be supposed, for pur- 

 poses of illustration, that it has been decided that ten of the stand- 



