Data-Level Issues
3.1 EXERCISES
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3.1 Measures of Center and Location
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Chapter 3 117b. Interpret your findings in part a.
c. Construct a box and whisker plot for the chickens’
weights and determine the distribution’s shape for the chickens’ weights, which will help justify the manufacturer’s suspicion.
3-10. Vistaprint is a digital printing company that prints items like business cards, calendars, and posters. It owns a certain number of printing machines. To ensure the machines operate properly, the factory supervisor conducts a procedural check every month. One item on her checklist is the machine temperature and ensuring that the temperature for all machines is between 50°C and 70°C. The following is a random selection of machine temperatures (in °C) recorded by her:
58 68 55 51 65 72 58 54
63 59 52 50 61 61 56 70
64 68 59 52 59 63 71 62
a. Compute the average machines’ temperatures recoded by the factory supervisor.
b. Compute the median machines’ temperatures recoded by the factory supervisor.
c. Determine the mode for machines’ temperatures.
d. Discuss your findings in parts a to c. Determine whether the machines’ temperatures are under control.
3-11. The La Costa Corporation operates five manufacturing plants in South America. The company tracks the medical costs that are directly attributed to accidents that occur at the plants each year. The following data show the medical costs (in U.S. dollars) at each plant for the most recent year along with the number of employees who work at each plant:
Medical Cost $7,400 $14,400 $12,300 $6,200 $3,100
Employees 123 402 256 109 67
a. Compute the weighted average for the annual medical costs at the five plants using the numbers of employees as the weights.
b. Explain why La Costa would want to use a weighted average in this situation rather than a simple average of the five medical cost values.
3-12. A librarian for Monfast University is checking the number of books borrowed by university students. He recorded the daily number of books borrowed by students during the past 30 days. The data are shown as follows:
20 8 37 25 10 16 5 43 39 31
30 41 19 36 27 14 11 33 42 7
15 29 34 17 30 32 21 12 35 28
Compute and interpret the mean, median, and mode for the number of books borrowed by students. Based on your findings, determine the distribution’s shape for the
daily number of books borrowed by students at Monfast University.
3-13. Toys “R” Us, Inc., is the leading store for children’s toys and other play material. The company’s financial officer is determining the previous month’s sales revenues. The following data are a selection of 30 outlets’ sales revenue (in $ thousands) record:
25 46 33 35 18 27 37 40 28 38
37 41 25 29 36 32 35 24 30 37
26 33 37 41 29 37 21 44 19 22
a. Compute the mean, median, and mode for these data.
b. Based on the result of part a, indicate whether the shape of the distribution is symmetric or skewed.
c. Construct a box and whisker plot for the sample data. Compare it with your answer to part b. Discuss your findings.
3-14. Samara Hauser is planning to buy a new car and she hopes to save on her expenses in petrol. Thus, before her purchase, she studied the mileage (in km) a car can travel at full tank oil capacity (in liters). The data are documented as follows:
Car Mileage (km) Oil Capacity (l)
1 465 40
2 423 38
3 360 41
4 455 36
5 398 43
a. Compute the average mileage (mean) for the cars and their respective mileage per liter.
b. Based on your findings in part a, which would be the best choice for Samara?
3-15. To obtain the average retail cost of a 55″ HD flat- screen TV in 2015, a survey yielded the following data (in U.S. dollars):
606.70 558.12 625.82 533.70 464.37 511.15 400.56 538.20 531.64 632.14 474.86 567.46 588.39 528.78 610.32 564.71 912.68 475.87 545.25 589.15
a. Calculate the mean cost for these data.
b. Examine the data presented. Choose an appropriate measure of the center of the data, justify the choice, and calculate the measure.
3-16. The following table exhibits base salary data obtained from a survey of over 170 benchmark positions, including finance positions. It reports the salaries of a sample of 25 human resource directors for mid-sized firms. Assume the data are in thousands of dollars.
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118 Chapter 3
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Describing Data Using Numerical Measures173.1 171.2 141.9 112.6 211.1 156.5 145.4 134.0 192.0 185.8 168.3 131.0 214.4 155.2 164.9 123.9 161.9 162.7 178.8 161.3 182.0 165.8 213.1 177.4 159.3
a. Calculate the mean salary of the HR directors.
b. Based on measures of the center of the data, determine if the salary data are skewed.
c. Construct a box and whisker plot and summarize the characteristics of the salaries that it reveals.
3-17. One of the conditions for measuring health is having a healthy body weight. An ideal body weight range is based on the height, gender, and age of a person. A recent study on health selected two different women’s age groups, in the same height range. Their weights were recorded as follows:
Weight (kg)
Women Aged 55 Years Women Aged 65 Years
59.8 66.5
65.5 74.3
67.7 69.9
71.7 64.8
68.9 71.6
a. Calculate the average weight for both groups of women.
b. Based on the findings in part a, is there any difference between the two groups?
c. Would the values calculated in part a be considered as parameters or statistics? Explain.
Computer Software Exercises
3-18. Each year, Bloomberg Businessweek publishes information and rankings of master of business administration (MBA) programs. The data file MBA Analysis contains similar data on several variables for eight reputable MBA programs. The variables include pre– and post–MBA salary, percentage salary increase, undergraduate GPA, average Graduate Management Admission Test (GMAT) score, annual tuition, and expected annual student cost. Compute the mean and median for each of the variables in the database and write a short report that summarizes the data. Include any appropriate charts or graphs to assist in your report.
3-19. Dynamic random-access memory (DRAM) chips are routed through fabrication machines in an order that is referred to as a recipe. The data file DRAM Chips contains a sample of processing times, measured in fractions of hours, at a particular machine center for one chip recipe.
a. Compute the mean processing time.
b. Compute the median processing time.
c. Determine what the mode processing time is.
d. Calculate the 80th percentile for processing time.
3-20. Japolli Bakery tracks sales of its different bread products on a daily basis. The data for 22 consecutive days at one of its retail outlets in Nashville are in a file called Japolli Bakery. Calculate the mean, mode, and median sales for each of the bread categories and write a short report that describes these data. Use any charts or graphs that may be helpful in more fully describing the data. Include a box and whisker plot comparing all the categories of breads.
3-21. In an effort to track housing prices, the National Association of Realtors developed the Pending Home Sales Index (PHSI), a leading indicator for the housing market. An index of 100 is equal to the average level of contract activity during 2001, the first year to be analyzed. The file titled Pending contains the PHSI from December 2014 to December 2015 (source: https://ycharts.com/indicators/pending _home_sales_index).
a. Determine the mean and median for the PHSI from December 2014 through December 2015. Specify the shape of the PHSI’s distribution.
b. Calculate the first and third quartiles for the PHSI for the months December 2014 through December 2015.
3-22. A proposal in a South Carolina county calls for all homeowners over the age of 65 with incomes at or below the 20th percentile to get a reduction in property taxes. A random sample of 50 people over 65 was selected, and the household incomes (as reported on the most current federal tax return) were recorded. These data are in the file called Property Tax Incomes. Use these data to establish the income cutoff point to qualify for the property tax cut.
3-23. Suppose a random sample of 137 households in Detroit was taken as part of a study on annual household spending for food at home. The sample data are contained in the file Detroit Eats.
a. For the sample data, compute the mean and the median and construct a box and whisker plot.
b. Are the data skewed or symmetric?
c. Approximately what percent of the data values are between $2,900 and $3,250?
3-24. In order to practice law in Nebraska, individuals are required to pass the Nebraska bar exam. The exam is challenging, and most attorneys who attempt to take the exam spend a substantial amount of time studying.
The file Nebraska contains data on the number of hours spent studying for a sample of 50 individuals who took and passed the bar exam.
a. Construct a stem and leaf display. Indicate the shape of data displayed by the stem and leaf display.
b. Use measures that indicate the shape of the distribution. Do these measures give results that agree with the shape shown in part a?
c. Considering your answers to parts a and b, indicate which measure you would recommend using to indicate the center of the data.
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