42 SUMMARIZATION OF DATA Ch. 2 



conclude that they were more uniform in weight than those whose 

 weights are reported in Table 2.42. However, if the second group 

 has a mean weight of ^ = 50 grams, it then is apparent that CV = 

 100(15/50) = 30 per cent. Hence Professor Ibsen's guinea pigs had 

 less variability in weight at birth than the other group of guinea pigs 

 when account is taken of the fact that they were generally heavier. 



PROBLEMS 



1. Compute the coefficient of variation for each of the following and draw 

 appropriate conclusions : 



X (N. Y. Curb Issues): 4, 3, 88, 1, 108, 42, 1, 25, 18, 5, 3, 6, 2, 22, and 70; 

 Y (Bond Quotations): 88, 115, 104, 113, 119, 80, 66, 40, 31, 101, 48, 43, 100, 84, 

 and 15. 



2. Using the X i as -2, 5, 8, 3, 1, 0, -2, 4, 3, and 6, and using k = 2, demon- 

 strate the <r kX = k-a x . 



3. Suppose that a group of measurements of the yield of corn in a certain 

 area of Iowa had /x = 70 bushels per acre, with a = 10 bushels, whereas an area 

 in Kansas, growing the same variety of corn and employing the same agronomic 

 method of culture, gave yields with n = 40 bushels per acre and a = 8 bushels 

 per acre. Are the yields in that part of Iowa relatively more variable than 

 those in Kansas, less variable, or about the same, according to these data? 



4. Suppose that during a certain period of years the prices of a certain com- 

 modity averaged $1.25, with standard deviation of 25 cents. The prices of this 

 same commodity during another period averaged but 80 cents, with a standard 

 deviation of 10 cents. During which period were the prices of this commodity 

 relatively more stable? Give reasoning. 



5. Following are simulated breaking strengths of samples of concrete (in hun- 

 dreds of pounds per square inch) : 40, 65, 50, 33, 48, 57, 60, 52, 50, 46, 70, 55, 51, 

 41, 49, 53, 56, 44, 47. 50, 46, 53, and 55. Compute the coefficient of variation. 



6. In problems 7 and 8, section 2.1, for which direction finder were the read- 

 ings relatively less variable? Would that result bear on the choice of one 

 instrument over the other if such a choice were to be made? 



7. Use the data of Table 2.61 to determine if the birth weights of female 

 guinea pigs born during January and February were relatively more or less 

 variable than those of males born during the same period. 



8. Solve as in problem 7 for June and July considered together. 



9. Use Table 2.62 to determine if the four-day gains of the males born during 

 January, February, and March were relatively more or less uniform than those 

 of females born during the same period. 



10. Solve as in problem 9 for animals born during October, November, and 

 December. 



