Sec. 2.6 PERCENTILES, DECILES, AND QUARTILES 37 



The upper limit of the first decile is the same as the upper limit of 

 the tenth percentile, and similarly for the other deciles. The upper 

 limits of the first, second, and third quartiles are the same as the 

 upper limits of the twenty-fifth, fiftieth, and seventy-fifth percentiles. 

 It should be clear that the median is the upper limit of the second 

 quartile. 



It is traditional to designate the upper limits of the first and third 

 quartiles as Qi and Q 3 , respectively, even though the term quartile 

 may be used differently from the way they are used in this book, as 

 was mentioned earlier in a footnote. 



PROBLEMS 



1. Following are the average temperatures for July in Topeka, Kansas, from 

 1901 to 1930, inclusive, in degrees Fahrenheit: 86.6, 77.0, 77.6, 75.0, 74.1, 74.8, 

 78.7, 76.0, 78.0, 79.4, 78.8, 79.9, 81.8, 80.2, 74.0, 81.9, 80.4, 78.0, 81.6, 76.8, 79.8, 

 76.4, 79.0, 75.2, 78.6, 79.0, 76.6, 78.3, 79.0, and 82.4. Obtain Q ± , md, and Q 3 . 



2. Determine and interpret the limits of the second decile for the data of 

 problem 1. Also compute the median. Ans. 74.88 to 76.08; md = 78.65. 



3. What are the limits of the third quartile of the data of problem 6 of 

 section 2.1? 



4. What are the limits of the first quartile for the fly counts given in prob- 

 lem 6, section 2.4? Ans. to 8 inclusive. 



5. Calculate the limits on the ninth decile for the counts of problem 1, section 

 2.4. What information can you derive from these limits? 



6. Use Figure 2.61 on page 40 to determine the approximate sizes of Q x , md, 

 and Q 3 for the birth weights recorded in Table 2.61. What information about 

 the birth weights do these numbers give? Ans. 66, SI, 95 grams. 



7. Construct a frequency distribution table and a graph for the 4-day gains 

 of Table 2.62 and compute the mean gain. 



8. Determine the limits on the 10th percentile of the 4-day gains of Table 

 2.62 and interpret these numbers statistically. Ans. —30 to —1.7, inclusive. 



9. Construct a relative cumulative frequency distribution table for the birth 

 weights listed in Table 2.61, using the class limits indicated in Figure 2.61. 



10. Suppose that a student entering college takes the following tests: a 

 general psychological test, a reading test, a mathematics aptitude test, a social 

 science aptitude test, and a physical science aptitude test. If his respective 

 percentile ratings are 90, 87, 50, 92, and 63, what advice would you give him 

 regarding a choice of a curriculum, assuming that you have faith in these tests? 

 Explain your reasoning. 



11. Determine the lower limit of the upper (tenth) decile for the ACE scores 

 of Table 2.01. 



