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

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84 CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA a. Produce a line plot of the data. b. Describe any trends that you detect. 2-70. The Minnesota State Fishing Bureau has contracted with a university biologist to study the length of walleyes (fish) caught in Minnesota lakes. The biologist has collected data on a sample of 1,000 fish caught and developed the following relative frequency distribution: Class Length (inches) Relative Frequency f i 8 to less than 10 .22 10 to less than 12 .15 12 to less than 14 .25 14 to less than 16 .24 16 to less than 18 .06 18 to less than 20 .05 20 to less than 22 .03 a. Construct a frequency distribution from this relative frequency distribution and then produce a histogram based on the frequency distribution. b. Construct a pie chart from the relative frequency distribution. Discuss which of the two graphs, the pie chart or the histogram, you think is more effective in presenting the fish length data. 2-71. The following data represent the commuting distances for employees of the Pay-and-Carry Department store. a. The personnel manager for Pay-and-Carry would like you to develop a frequency distribution and histogram for these data. b. Develop a stem and leaf diagram for these data. c. Break the data into three groups (under 3 miles, 3 and under 6 miles, and 6 and over). Construct a pie chart to illustrate the proportion of employees in each category. Commuting Distance (miles) their call is answered by the central switchboard. The company would like to have at most 2% of the callers wait two minutes or more. The company’s calling service has provided the following data showing how long each of last month’s callers spent on hold: Class Number Less than 15 seconds 456 15 to less than 30 seconds 718 30 to less than 45 seconds 891 45 to less than 60 seconds 823 60 to less than 75 seconds 610 75 to less than 90 seconds 449 90 to less than 105 seconds 385 105 to less than 120 seconds 221 120 to less than 150 seconds 158 150 to less than 180 seconds 124 180 to less than 240 seconds 87 More than 240 seconds 153 a. Develop a relative frequency distribution and ogive for these data. b. The company estimates it loses an average of $30 in business from callers who must wait two minutes or more before receiving assistance. The company thinks that last month’s distribution of waiting times is typical. Estimate how much money the company is losing in business per month because people have to wait too long before receiving assistance. 2-73. The regional sales manager for American Toys, Inc. recently collected data on weekly sales (in dollars) for the 15 stores in his region. He also collected data on the number of salesclerk work hours during the week for each of the stores. The data are as follows: 3.5 2.0 4.0 2.5 0.3 1.0 12.0 17.5 3.0 3.5 6.5 9.0 3.0 4.0 9.0 16.0 3.5 0.5 2.5 1.0 0.7 1.5 1.4 12.0 9.2 8.3 1.0 3.0 7.5 3.2 2.0 1.0 3.5 3.6 1.9 2.0 3.0 1.5 0.4 6.4 11.0 2.5 2.4 2.7 4.0 2.0 2.0 3.0 d. Referring to part c, construct a bar chart to depict the proportion of employees in each category. 2-72. A computer software company has been looking at the amount of time customers spend on hold after Store Sales Hours Store Sales Hours 1 23,300 120 9 27,886 140 2 25,600 135 10 54,156 300 3 19,200 96 11 34,080 254 4 10,211 102 12 25,900 180 5 19,330 240 13 36,400 270 6 35,789 190 14 25,760 175 7 12,540 108 15 31,500 256 8 43,150 234
CHAPTER 2 • GRAPHS, CHARTS, AND TABLES—DESCRIBING YOUR DATA 85 a. Develop a scatter plot of these data. Determine which variable should be the dependent variable and which should be the independent variable. b. Based on the scatter plot, what, if any, conclusions might the sales manager reach with respect to the relationship between sales and number of clerk hours worked? Do any stores stand out as being different? Discuss. Computer Database Exercises 2-74. USA Today reported (Jefferson Graham, “Looks like the new iPod’s a hit,” September 19, 2005) that Apple had 74% of the digital music device market, according to researcher The NPD Group. The NPD Group provides global sales and marketing information that helps clients make more informed, fact-based decisions in order to optimize their businesses. The data in the file entitled Digital provide the brand of digital devices owned by a sample of consumers that would produce the market shares alluded to in the article. Produce a pie chart that represents the market shares obtained from the referenced sample. Indicate the market shares and the identity of those manufacturers in the pie chart. 2-75. The file Home-Prices contains information about single-family housing prices in 100 metropolitan areas in the United States. a. Construct a frequency distribution and histogram of 1997 median single-family home prices. Use the 2 k n guideline to determine the appropriate number of classes. b. Construct a cumulative relative frequency distribution and ogive for 1997 median single-family home prices. c. Repeat parts a and b but this time use half again as many class intervals as recommended by the 2 k n guideline. What was the impact of using more class intervals? 2-76. Elliel’s Department Store tracks its inventory on a monthly basis. Monthly data for the years 1996– 2000 are in the file called Elliels. a. Construct a line chart showing the monthly inventory over the five years. Discuss what this graph implies about inventory. b. Sum the monthly inventory figures for each year. Then present the sums in bar chart form. Discuss whether you think this is an appropriate graph to describe the inventory situation at Elliels. 2-77. The Energy Information Administration (EIA) surveys the price of diesel fuel. The EIA-888 is a survey of diesel fuel outlet prices from truck stops and service stations across the country. It produces estimates of national and regional prices. The diesel fuel prices that are released are used by the trucking industry to make rate adjustments in hauling contracts. The file entitled Diesel$ contains the average on-highway diesel prices for each of 53 weeks from September 27, 2004 to September 26, 2005. a. Construct a histogram with 11 classes beginning at $1.85. b. Are there any data points that are unusually larger than the rest of the data? In which classes do these points occur? What is the interpretation of this phenomenon? 2-78. The Energy Information Administration published a press release on September 26, 2005 (Paula Weir and Pedro Saavedra, “Two Multi-Phase Surverys That Combine Overlapping Sample Cycles at Phase I”). The file entitled Diesel$ contains the average on-highway diesel prices for each of 53 weeks from September 27, 2004 to September 26, 2005. It also contains equivalent information for the state of California, recognized as having the highest national prices. a. Construct a chart containing line plots for both the national average and California’s diesel prices. Describe the relationship between the diesel prices in California versus the national average. b. In what week did the California average diesel price surpass $3.00 a gallon? c. Determine the smallest and largest price paid in California for a gallon of diesel. At what weeks did these occur? Use this information to project when California gas prices might exceed $4.00, assuming a linear trend between California diesel prices and the week in which they occurred. VIDEO CASE 3 Drive-Thru Service Times @ McDonald’s When you’re on the go and looking for a quick meal, where do you go? If you’re like millions of people every day, you make a stop at McDonald’s. Known as “quick service restaurants” in the industry (not “fast food”), companies such as McDonald’s invest heavily to determine the most efficient and effective ways to provide fast, high quality service in all phases of their business. Drive-thru operations play a vital role. It’s not surprising that attention is focused on the drive-thru process. After all,
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Chapter 2: Graphs, Charts, and Tables--Describing Your Data

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