Ch. 2 REVIEW PROBLEMS 45 



the manner indicated above. Following are the summaries of the 

 two samples: 



Sample 1 Sample 2 



Mean = 23.2, median = 19 Mean = 13.4, median = 10 



Standard deviation = 16.2, range = 45 Standard deviation = 9.7, range = 28 

 CV = 69.8 per cent CV = 72.4 per cent 



For these two samples, each of the five statistical measures is dif- 

 ferent again. Moreover, considering the fact that these fly counts 

 are generally smaller numbers than the ACE scores, the relative 

 differences are much larger between the two samples than was true 

 for the ACE scores. For example the mean for one sample of the 

 counts is almost twice the size of the mean of the other sample. Much 

 the same is true of each of the other measures except the coefficient 

 of variation. This is an illustration of the fact that a statistical study 

 of samples requires some information about the frequency distribu- 

 tions of the populations sampled. Hence this matter, and probability, 

 must be studied before more can be done about the analysis of sam- 

 pling data. These are the aims of chapters 3 and 4. 



REVIEW PROBLEMS 



1. The effectiveness of penicillin in controlling bacterial growth can be meas- 

 ured by the "inhibition zone" produced when a standard amount of penicillin is 

 properly added to a plate of agar containing the type of bacterial growth one 

 wishes to study. Following are 54 such determinations arranged in 9 groups 

 of 6 tests each. (From an article by Jackson W. Foster and H. Boyd Woodruff, 

 Journal oj Bacteriology , August, 1943.) Calculate the arithmetic mean of each 

 set of tests, and then compute the standard deviation of these nine means. 



Test 1 Test 2 Test 3 Test 4 Test 5 Test 6 Test 7 Test 8 Test 9 

 28.1 28.5 28.0 27.5 29.0 28.0 29.0 28.5 28.0 



2. Determine the range for each set of data in problem 1, and compute the 

 standard deviation for the set with the greatest range. 



Ans. 0.6, 1.0, 0.7, 1.0, 1.7, 0.6, 2.0, 1.0, 1.5; 0.88. 



3. If a list of the farm acreages in a certain county in Kansas forms a statis- 

 tical array of numbers from 35 to 4000; and if fi =600 and md = 350 acres: 



(a) Which average would you think might be more typical of the size of 

 farm in that county? 



(£>) Would you expect the high point of the frequency distribution to be 

 about over the mean, to its right, or to its left? Give reasons. 



