44 SUMMARIZATION OF DATA Ch. 2 



The following random sample of 50 scores from Table 2.01 was 

 obtained by the second method described above: 



131, 66, 117, 117, 145, 71, 118, 99, 128, 111, 95, 78, 88, 55, 86, 89, 97, 



98, 87, 80, 100, 76, 124, 89, 79, 101, 89, 156, 111, 98, 103, 68, 110, 76, 



99, 100, 102, 61, 50, 125, 92, 106, 63, 117, 124, 87, 95, 100, 58, and 99. 



These particular measurements were obtained by chance from among 

 many possible different sets of 50. This fact suggests that the theory 

 of probability is needed in the analysis of sampling data. 



It is found in the usual manner that the mean and the standard 

 deviation for the sample above are 96.28 and 22.55, respectively. 

 The range of scores in this sample is 106, the median is 98, and the 

 coefficient of variation is 23.4 per cent. It is known that these sta- 

 tistical measures are not likely to be exactly the same as the popula- 

 tion parameters, but it is to be hoped that they are not far from 

 those values. 



Another sample was drawn in the same manner as the sample just 

 described. The following were calculated for this second sample: 

 mean = 99.22, standard deviation = 27.30, range = 144, median = 

 100.5, and the coefficient of variation is 27.5 per cent. It is noted 

 that each of these statistical measures is different for the two samples, 

 yet only the ranges differ by a large percentage. It is typical of 

 random samples that they usually differ from each other in several 

 respects because the particular members of such samples are in the 

 sample by chance. It also is true that the sizes of such statistical 

 measures as the sampling mean will follow some predictable pattern 

 over considerable sampling experience. If this were not true, nothing 

 much could be learned from sampling. It will be seen in later chap- 

 ters that probability theory is needed to study these matters. 



To illustrate the effect of the type of population on the results 

 obtained from random sampling, consider two samples drawn from 

 the data in problem 1 at the end of section 2.4. For convenience, 

 samples of 10 numbers each were drawn even though this is a some- 

 what larger fraction of the population than was taken from Table 

 2.01. These samples were obtained by considering that the fly counts 

 were numbered serially from left to right, starting with the top row. 

 There are 148 fly counts in this population; hence a sample of 10 was 

 drawn by effectively drawing 10 numbers at random from among 

 the numbers 1, 2, 3, ... , 148. When these 10 ordinal numbers were 

 drawn, the corresponding fly counts were obtained by counting in 



