2-4. Exercises
1. Basic Exercises
Ex 1. ë€ìêłŒ ê°ì ë°ìŽí° ìžížê° ìë€.
a. 82ëČ짞 percentileì ê”ŹíëŒ.
b. 68ëČ짞 percentileì ê”ŹíëŒ.
[Solution]
Ex 2. ë€ìêłŒ ê°ì ë°ìŽí° ìžížê° ìë€.
a. 6.5 ê°ì percentile ììë„Œì ê”ŹíëŒ.
b. 7.7 ê°ì percentile ììë„Œì ê”ŹíëŒ.
[Solution]
Ex 3. ë€ìêłŒ ê°ì stem and leaf diagramìŒëĄ ííë ë°ìŽí° ìžížê° ìë€.
a. 75ì percentile ììë„Œ ê”ŹíëŒ.
b. 57ì percentile ììë„Œ ê”ŹíëŒ.
[ Solution ]
Ex 4. ë°ìŽí° ìžížì 90ëČ짞 percentileì 90%ì ê°ìê°? Why or Why not?
Ex 5. ë°ìŽí° ìžížì 29ëČ짞 percentileì 5ìŽë€.
a. êŽìžĄìčì ëȘ íŒìŒížê° 5ëłŽë€ ë ììê°?
b. êŽìžĄìčì ëȘ íŒìŒížê° 5ëłŽë€ ë í°ê°?
Ex 6. ë°ìŽí° ìžížì 54ëČ짞 percentileìŽ 98.6ìŽë€.
a. êŽìžĄìčì ëȘ íŒìŒížê° 98.6 ëłŽë€ ë ììê°?
b. êŽìžĄìčì ëȘ íŒìŒížê° 98.6 ëłŽë€ ë í°ê°?
Ex 7. í ë°ìŽí° ìžížì 29ëČìš° percentileìŽ 5ìŽêł , 79ëČ짞 percentileìŽ 10ìŽë€. 5ì 10 ìŹìŽìë êŽìžĄìčì ëȘ íŒìŒížê° íŹíšëëê°?
Ex 8. í ë°ìŽí° ìžížì 40ëČìš° percentileìŽ 125ìŽêł , 82ëČ짞 percentileìŽ 158ìŽë€. 125ì 158 ìŹìŽìë êŽìžĄìčì ëȘ íŒìŒížê° íŹíšëëê°?
Ex 9. Ex. 2)ì ë°ìŽí° ìžížì ëíìŹ five-number summaryì IQRì ê”ŹíëŒ. ê·žëŠŹêł box plotì ìì±íëŒ.
Ex 10. Ex. 3)ì ìstem and leaf diagramìŒëĄ ííë ë°ìŽí° ìžížì ëíìŹ five-number summaryì IQRì ê”ŹíëŒ. ê·žëŠŹêł box plotì ìì±íëŒ.
Ex 11. ë€ìì data frequency tableëĄ ííë ë°ìŽí° ìžížì five-number summaryì IQRì ê”ŹíëŒ. ê·žëŠŹêł box plotì ìì±íëŒ.
Ex 12. ë€ìì data frequency tableëĄ ííë ë°ìŽí° ìžížì five-number summaryì IQRì ê”ŹíëŒ. ê·žëŠŹêł box plotì ìì±íëŒ.
Ex 13. ë€ìì íëłž ë°ìŽí° ìžížì ìë ê° ìžĄì ìčì z-scoreë„Œ ê”ŹíëŒ.
Ex 14. ë€ìì íëłž ë°ìŽí° ìžížì ìë ê° ìžĄì ìčì z-scoreë„Œ ê”ŹíëŒ.
Ex 15. ë€ìì data frequency tableì ê°ë íëłžìŽ íê· 3, íì€ížì°š 2.71ì ê°ëë€. íëłžì ìë ê° ììčì z-scoreë„Œ ê”ŹíëŒ.
Ex 16. ë€ìì data frequency tableì ê°ë íëłžìŽ íê· 3, íì€ížì°š 2.71ì ê°ëë€. íëłžì ìë ê° ììčì z-scoreë„Œ ê”ŹíëŒ.
Ex 17. ë€ìêłŒ ê°ì ëȘšì§ëšìŽ ìë€.
a. ëȘšíê· ì ê”ŹíëŒ().
b. ëȘšë¶ì°ì ê”ŹíëŒ().
c. ëȘš íì€ížì°šë„Œì ê”ŹíëŒ().
d. ëȘšì§ëš ë°ìŽí° ìžížì ê° ììčì ëí z-scoreë„Œ ê”ŹíëŒ.
Ex 18. ë€ìêłŒ ê°ì ëȘšì§ëšìŽ ìë€.
a. ëȘšíê· ì ê”ŹíëŒ().
b. ëȘšë¶ì°ì ê”ŹíëŒ().
c. ëȘš íì€ížì°šë„Œ ê”ŹíëŒ().
d. ëȘšì§ëš ë°ìŽí° ìžížì ê° ììčì ëí z-scoreë„Œ ê”ŹíëŒ.
Ex 19. íëłž íê· ìŽ 10, íì€ížì°šê° 3ìž xì z-score ê°ìŽ 2ìŽë€. xë„Œ ê”ŹíëŒ.
Ex 20. íëłž íê· ìŽ 10, íì€ížì°šê° 3ìž xì z-score ê°ìŽ -1ìŽë€. xë„Œ ê”ŹíëŒ.
Ex 21. ëȘš íê· ìŽ 2.3, íì€ížì°šê° 1.3ìž xì z-score ê°ìŽ 2ìŽë€. xë„Œ ê”ŹíëŒ.
Ex 22. ëȘš íê· ìŽ 2.3, íì€ížì°šê° 1.3ìž xì z-score ê°ìŽ -1.2ìŽë€. xë„Œ ê”ŹíëŒ.
2. Applications Exercises
Ex 24. The weekly sales for the last 20 weeks in a kitchen appliance store for an electric automatic rice cooker are
Find the percentile rank of 15.
If the sample accurately reflects the population, then what percentage of weeks would an inventory of 15 rice cookers be adequate?
Ex 25. The table shows the number of vehicles owned in a survey of 52 households.
Find the percentile rank of 2.
If the sample accurately reflects the population, then what percentage of households have at most two vehicles?
Ex 26. For two months Cordelia records her daily commute time to work each day to the nearest minute and obtains the following data:
Cordelia is supposed to be at work at 8:00 a.m. but refuses to leave her house before 7:30 a.m.
Find the percentile rank of 30, the time she has to get to work.
Assuming that the sample accurately reflects the population of all of Cordeliaâs commute times, use your answer to part (a) to predict the proportion of the work days she is late for work.
Ex 27. The mean score on a standardized grammar exam is 49.6; the standard deviation is 1.35. Dromio is told that the z-score of his exam score is â1.19.
Is Dromioâs score above average or below average?
What was Dromioâs actual score on the exam?
Ex 28. A random sample of 49 invoices for repairs at an automotive body shop is taken. The data are arrayed in the stem and leaf diagram shown. (Stems are thousands of dollars, leaves are hundreds, so that for example the largest observation is 3,800.)
For these data, , .
Find the z-score of the repair that cost $1,100.
Find the z-score of the repairs that cost $2,700.
Ex 29. The stem and leaf diagram shows the time in seconds that callers to a telephone-order center were on hold before their call was taken.
Find the quartiles.
Give the five-number summary of the data.
Find the range and the IQR.
3. Additional Exercises
Ex 29. stem and leaf diagram
a. quartiles
b. five-number summary
c. range and IQR
Ex 30. stem and leaf diagram
a. percentile rank of 800
b. percentile rank of 3,200
Ex 31. Frequency table -> five-number summary
Ex 32. Frequency table -> five-number summary
Ex 33. stem and leaf diagram
a. three quartiles
b. IQR
c. five-number summary
Ex 34. Determine whether the following statement is true. âIn any data set, if an observation x1 is greater than another observation x2, then the z-score of x1 is greater than the z-score of x2.â
Ex 35. z-score : ëčê” of the z-score of x1 and the z-score of x2.
Ex 36. z-score
Ex 37. z-score : ëčê” of the z-score of x1 and the z-score of x2.
4. Large Data Set Exercises
Ex 38. Large Data Set 1 lists the SAT scores and GPAs of 1,000 students.
Compute the three quartiles and the interquartile range of the 1,000 SAT scores.
Compute the three quartiles and the interquartile range of the 1,000 GPAs.
Ex 39. Large Data Set 10 records the scores of 72 students on a statistics exam.
Compute the five-number summary of the data.
Describe in words the performance of the class on the exam in the light of the result in part (a).
Ex 40. Large Data Sets 3 and 3A list the heights of 174 customers entering a shoe store.
Compute the five-number summary of the heights, without regard to gender.
Compute the five-number summary of the heights of the men in the sample.
Compute the five-number summary of the heights of the women in the sample.
[ Solution ]
Ex 41. Large Data Sets 7, 7A, and 7B list the survival times in days of 140 laboratory mice with thymic leukemia from onset to death.
Compute the three quartiles and the interquartile range of the survival times for all mice, without regard to gender.
Compute the three quartiles and the interquartile range of the survival times for the 65 male mice (recorded as gender = "M" in Large Data Set 7).
Compute the three quartiles and the interquartile range of the survival times for the 75 female mice (recorded as gender = "F" in Large Data Set 7B).
Last updated
Was this helpful?