Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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56 CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 25 CFOs. Assume that data are in thousands of dollars. 173.1 171.2 141.9 112.6 211.1 156.5 145.4 134.0 192.0 185.8 168.3 131.0 214.4 155.2 164.9 123.9 161.9 162.7 178.8 161.3 182.0 165.8 213.1 177.4 159.3 a. Using 11 classes, construct a cumulative frequency distribution. b. Determine the proportion of CFO salaries that are larger than $175,000. c. Determine the proportion of CFO salaries that are at most $205,000 and at least $135,000. 2-16. The San Diego Union Tribune reported (“Mortgage Interest Rates Rise,” September 16, 2005) that the 30-year fixed-rate mortgage rates had risen to an average of 5.74% in September 2005. A sample of mortgage rates in the San Diego area produced the following interest rates: 5.84 5.73 5.58 5.69 5.84 5.68 5.73 5.79 5.77 5.67 5.76 5.70 5.70 5.66 5.71 5.80 5.81 5.75 5.81 5.78 5.79 5.77 5.73 5.67 5.74 5.76 5.76 5.74 5.73 5.71 5.71 5.72 5.80 5.69 5.88 5.70 5.75 5.75 5.68 5.72 5.70 5.67 5.83 5.76 5.80 a. Construct a histogram with eight classes beginning at 5.58. b. Determine the proportion of mortgage rates that are at least 5.74%. c. Generate an ogive for this data. Computer Database Exercises 2-17. The Franklin Tire Company is interested in demonstrating the durability of its steel-belted radial tires. To do this, the managers have decided to put four tires on 100 different sport utility vehicles and drive them throughout Alaska. The data collected indicate the number of miles (rounded to the nearest 1,000 miles) that each of the SUVs traveled before one of the tires on the vehicle did not meet minimum federal standards for tread thickness. The data file is called Franklin. a. Construct a frequency distribution and histogram using 8 classes. Use 51 as the lower limit of the first class. b. The marketing department wishes to know the tread life of at least 50% of the tires, the 10% that had the longest tread life, and the longest tread life of these tires. Provide this information to the marketing department. Also provide any other significant items that point out the desirability of this line of steelbelted tires. c. Construct a frequency distribution and histogram using 12 classes, using 51 as the lower limit of the first class. Compare your results with those in parts a and b. Which distribution gives the best information about the desirability of this line of steel-belted tires? Discuss. 2-18. The United States Golf Association recently conducted a survey of its members. Among other questions, the members were asked to indicate the number of 18-hole rounds that they played last year. Data for a sample of 294 members is provided in the data file called golf survey. a. Using the 2 k n guideline, what is the minimum number of classes that should be used to display these data in a grouped data frequency distribution? b. Referring to part a, what should the class width be, assuming you round the width up to nearest integer? c. Referring to parts a and b, develop a grouped data frequency distribution for these golf data. d. Based on your answer to part c, construct and interpret a frequency histogram for the data. 2-19. J.D. Power and Associates’ annual customersatisfaction survey, the Automotive Performance, Execution and Layout (APEAL) Study SM , in its 10th year, was released on September 21, 2005. The study measures owners’ satisfaction with the design, content, layout, and performance of their new vehicles. A file entitled APEAL contains the satisfaction ratings for 2005 for each make of car. a. Construct a histogram for the APEAL ratings that starts at 825 and has class widths of 10. b. The past industry average APEAL rating was 855. What does the 2005 data suggest in terms of the relative satisfaction with the 2005 models? c. Determine if any class is vacant and indicate what that would signify with respect to these data. 2-20. Ars Technia, LLD published a news release (Eric Bangeman, “Dell still king of market share,” January 18, 2005) that presented the results of a study concerning the world market share for the major manufacturers of personal computers. It indicated that Dell held 17.9% of this market. The file entitled PCMarket contains a sample of the market shares alluded to in the article.
CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 57 a. Construct a histogram from this set of data and identify the market shares for each of the listed manufacturers. b. Excluding the data referred to as “other,” determine the total market share of the manufacturers that have headquarters in the United States. 2-21. Orlando, Florida, is a vacation destination for travelers from across the United States and around the world. As a result, the Orlando International Airport is very busy throughout the year. The Greater Orlando Airport Authority (GOAA) maintains a variety of data pertaining to airport operations. For example, the GOAA tracks the number of people who get on and off airplanes by airline. For the year 2004, these data are in a file called Orlando Airport 2004. These data can also be located on the airport’s Web site at sun6.dms. state.fl.us/goaa. Suppose the airport manager is interested in analyzing the passenger data. In particular, she wishes you to help her with the following. (Hint: Use the variable called Total.) a. Using the 2 k n guideline, what is the minimum number of classes that should be used to display these data in a grouped data frequency distribution? b. Referring to part a, what should the class width be, assuming you round the width up to nearest 1,000 passengers? c. Referring to parts a and b, develop a grouped data frequency distribution for these airport data. d. Based on your answer to part c, construct and interpret a frequency histogram for the data. 2-22. The manager of AJ’s Fitness center, a full-service heath and exercise club, recently conducted a survey of 1,214 members. The objective of the survey was to determine the satisfaction level of his club’s customers. In addition, the survey asked for several demographic factors such as age and gender. The data from the survey are in a file called AJFITNESS. a. One of the key variables is “Overall Customer Satisfaction.” This variable is measured on an ordinal scale as follows: 5 very satisfied 4 satisfied 3 neutral 2 dissatisfied 1 very dissatisfied Develop a frequency distribution for this variable and discuss the results. b. Develop a joint relative frequency distribution for the variables “Overall Customer Satisfaction” and “Typical of Visits Per Week.” Discuss the results. 2-23. The file German Coffee contains data on individual coffee consumption (in kg) for 144 randomly selected German coffee drinkers. a. Construct a data array of the coffee consumption data. b. Construct a frequency distribution of the coffee consumption data. Within what class do more of the observations fall? c. Construct a histogram of the coffee consumption data. Briefly comment on what the histogram reveals concerning the data. d. Develop a relative frequency distribution and a cumulative relative frequency distribution of the coffee data. What percentage of the coffee drinkers sampled consumes 8.3 kg or more annually? Bar Chart A graphical representation of a categorical data set in which a rectangle or bar is drawn over each category or class. The length or height of each bar represents the frequency or percentage of observations or some other measure associated with the category. The bars may be vertical or horizontal. The bars may all be the same color or they may be different colors depicting different categories. Additionally, multiple variables can be graphed on the same bar chart. Business Application 2.2 Bar Charts, Pie Charts, and Stem and Leaf Diagrams Bar Charts Section 2-1 introduced some of the basic tools for describing numerical variables, both discrete and continuous, when the data are in their raw form. However, in many instances, you will be working with categorical data or data that have already been summarized to some extent. In these cases, an effective presentation tool is often a bar chart. NEW CAR SALES The automobile industry is a significant part of the U.S., Japanese, and German economies. When car sales are up, the economies of these countries are up, and vice-versa. Table 2.8 displays data showing the total number of cars sold in March 2005,
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