104 CHAPTER 3 Describing Data Using Numerical Measures 3-5. A random sample of the miles driven by 20 rental car customers is shown as follows: 90 85 100 150 125 75 50 100 75 60 35 90 100 125 75 85 50 100 50 80 Develop a box and whisker plot for the sample data. 3-6. Examine the following data: 23 65 45 19 35 28 39 100 50 26 25 27 24 17 12 106 23 19 39 70 20 18 44 31 a. Compute the quartiles. b. Calculate the 90th percentile. c. Develop a box and whisker plot. d. Calculate the 20th and the 30th percentiles. 3-7. Consider the following data that represent the commute distances for students who attend Emory University: 3.1 4.7 8.4 11.6 12.1 13.0 13.4 16.1 17.3 20.8 22.8 24.3 26.2 26.6 26.7 31.2 32.2 35.8 35.8 39.8 a. Determine the 80th percentile. b. Determine numbers that are the 25th and 75th percentiles. c. Determine a number that qualies as a median for these data. 3-8. A professor wishes to develop a numerical method for giving grades. He intends to base the grade on homework, two midterms, a project, and a nal examination. He wishes the final exam to have the largest influence on the grade. He wants the project to have 10%, each midterm to have 20%, and the homework to have 10% of the inuence of the semester grade. a. Determine the weights the professor should use to produce a weighted average for grading purposes. b. For a student with the following grades during the quarter, calculate a weighted average for the course: Instrument Final Project Midterm 1 Midterm2 Homework Percentage Grade 64 98 67 63 89 c. Calculate an (unweighted) average of these ve scores and discuss why the weighted average would be preferable here. Business Applications 3-9. The manager for the Jiffy Lube in Saratoga, Florida, has collected data on the number of customers who agreed to purchase an air lter when they were also having their oil changed. The sample data are shown as follows: 21 19 21 19 19 20 18 12 20 19 17 14 21 22 25 21 22 23 10 19 25 14 17 18 a. Compute the mean, median, and mode for these data. b. Indicate whether the data are skewed or symmetrical. c. Construct a box and whisker plot for these data. Referring to your answer in part b, does the box plot support your conclusion about skewness? Discuss. 3-10. During the past few years, there has been a lot of discussion about the price of university textbooks. The complaints have come from many places, including students, faculty, parents, and even government ofcials. The publishing companies have been called on to explain why textbooks cost so much. Recently, one of the major publishing companies was asked to testify before a congressional panel in Washington, DC. As part of the presentation, the president of the company organized his talk around four main areas: production costs, author royalties, marketing costs, and bookstore markup. He used one of his company's business statistics texts as an example when he pointed out the production costsincluding editing, proong, printing, binding, inventory holding, and distribution come to about $32 per book sold. Authors receive $12 per copy for the hundreds of hours of creative work in writing the book and supplementary materials. Marketing costs are pegged at about $5 per copy sold and go to pay for the book sales force and examination copies sent to professors. The book is then sold to bookstores for $70 per copy, a markup on costs of about 40% to cover overhead and the publishing costs associated with many upper-division, low-market texts that lose money for the company. Once university bookstores purchase the book, they mark it up, place it on the shelf, and sell it to the student. If books go unsold, they are returned to the publisher for a full refund. The following data reect the dollar markup on the business statistics text for a sample of 20 college bookstores: $33 $32 $42 $31 $3 1 $37 $37 $34 $47 $3 1 $42 $29 $36 $32 $25 $29 $47 $26 $32 $40 3. Compute the mean markup on the business statistics text by university bookstores in the sample. b. Compute the median markup. c. Determine the mode markup. (1. Write a short paragraph discussing the statistics computed in parts ac. 3-11. The Xang Corporation operates ve clothing suppliers in China to provide merchandise for Nike. Nike recently sought information from the ve plants. One variable for which data were collected was the total money (in US. dollars) the company spent on medical support for its employees in the rst three months of the year. Data on number of