Ch 2

CHAPTER 2

Describing Data: Graphical

Multiple-Choice Questions

1. Which of the following variables is an example of a categorical variable?

A) The amount of money you spend on eating out each month.B) The time it takes you to write a test.C) The geographic region of the country in which you live.D) The weight of a cereal box.ANSWER: C

2. Which of the following would be an example of a discrete random variable?

A) The monthly electric bill for a local business.B) The number of people eating at a local café between noon and 2:00 p.m.C) The amount of time it takes for a worker to complete a complex task.D) The percentage of people living below the poverty level in a Boston.ANSWER: B

3. What is the correct ranking of data from weakest or lowest type to strongest or higher type?

A) Nominal, ordinal, interval and ratioB) Ordinal, nominal, interval and ratioC) Interval, nominal, ratio and ordinalD) Nominal, interval, ordinal, and ratioANSWER: A

4. Which of the following statements is incorrect?

A) Ordinal data may be described as qualitative.B) Nominal data may be described as quantitative.C) A categorical variable may produce ordinal data.D) A discrete numerical variable may produce ratio scale data.ANSWER: B

11

Chapter 2

5. The length of time it takes to assemble a particular electronic component varies from an employee to another. Management has collected the time (in minutes) it took 20 different employees to assemble the component. The information is summarized in the following frequency distributions generated by Excel.

Which of the following statements is true?

A) It took 50% of all workers exactly 15 minutes to assemble the component.B) It took 100% of all workers longer than 25 minutes to assemble the component.C) Eleven workers assembled the component in 20 minutes or less.D) Seven workers took 25 minutes or longer to assemble the component.ANSWER: C

6. Consider the following frequency distributions generated by Excel. What is the missing cumulative % value identified by asterisk?

A) 60.00%B) 5.00%C) 100%D) 90%ANSWER: D

7. Consider the following frequency distribution generated by Excel. What is the missing frequency value identified by asterisk?

Bin Frequency Cumulative %584 1 4.00%

1774.4 * 64.00%2964.8 4 80.00%4155.2 3 92.00%5345.6 1 96.00%More 1 100.00%

A) 3B) 15C) 16D) 25ANSWER: B

12

Bin Frequency Cumulative %10 1 5.00%15 9 50.00%20 1 55.00%25 7 90.00%

More 2 100.00%

Bin Frequency Cumulative %12.8 1 5.00%41.6 5 30.00%70.4 6 60.00%99.2 6 *More 2 100.00%


8. Data on the monthly expenses (in $) submitted by 15 people on a firm’s sales staff are summarized in the following stem-and-leaf display.

Stem-and-leafDollars N = 25Leaf Unit = 10.02 2 5 7(7) 3 1 1 4 5 6 7 85 4 2 2 4 5 91 5 1

Which of the following statements is not true?

A) The leaf 7 represents $70.B) The number 5 in the left-hand column tells us that five people had expenses between

$400 and $499.C) The parentheses around the number 7 in the left-hand column tell us that most of the

employees had expenses between $300 and $399.D) There was one employee who spent at least $510.ANSWER: C

9. A sample of 30 professional men was asked to estimate their yearly expenditures on clothes for work. The data are summarized in the following stem-and-leaf display.

Stem-and-leafDollars N = 30Leaf Unit = 10.02 5 0 4 85 6 0 0 2 4 5 9(11) 7 0 0 2 2 3 3 5 5 7 7 86 8 0 0 2 3 7 8 3 9 2 2 71 10 0

What percentage of these men spent more than $900 on professional attire?

A) 87.7%B) 13.3%C) 16.7%D) 83.3%ANSWER: B

10. Professor Anderson graduated from the University of Michigan with a code value = 1 while Professor Jackson graduated from Michigan State with a code value = 2. The scale of measurement likely represented by this information is:

A) nominalB) ordinalC) intervalD) ratioANSWER: A

13

Chapter 2

11. Consider the following frequency distribution generated by Excel. What proportion of these values are less than 63?

Bin Frequency Cumulative %26 0 0.00%

44.5 5 25.00%63 7 60.00%

81.5 1 65.00%More 7 100.00%

A) 25%B) 60%C) 65%D) 35%ANSWER: A

12. Companies are often interested in knowing how customers learned about their products. They often solicit this information on mail-in warranty cards. The customers’ responses for a particular product were gathered and the data are presented in the pie chart below.

What percentage of respondents learned about the product through television or the Internet?

A) 12%B) 39%C) 51%D) 100%ANSWER: C

13. Pareto’s result is applied to a wide variety of behavior over many systems. It is sometimes referred to as the

A) “20-80” RuleB) “80-20” RuleC) “10-90” RuleD) “90-10” RuleANSWER: B

QUESTIONS 14 THROUGH 17 ARE BASED ON THE FOLLOWING INFORMATION:

14


In a recent survey, respondents were classified according to their gender, marital status, and geographic location. These data are summarized in the following cross table:

14. What percentage of the respondents were unmarried people?

A) 0.620B) 0.305C) 0.510D) 0.543 ANSWER: D

15. What percentage of the respondents were unmarried people from the Midwest?

A) 0.195B) 0.543C) 0.464D) 0.359ANSWER: A

16. What percentage of the respondents were single people from the Northeast?

A) 0.543B) 0.073 C) 0.475D) 0.134ANSWER: B

17. What percentage of the respondents were married people from the South?

A) 0.114B) 0.169C) 0.352D) 0.078 ANSWER: D

QUESTIONS 18 THROUGH 20 ARE BASED ON THE FOLLOWING INFORMATION:

15

Single Male

Single Female

Married Male

Married Female

Row Total

Northeast 12 17 22 10 61

South 31 26 8 23 88

Midwest 45 33 52 38 168

West 34 19 24 13 90

Column Total 122 95 99 84 400

Chapter 2

In a recent marketing experiment, consumers were given one of four different types of dishwashing detergent and asked to use it for a month. At the end of that time they were asked to rate the detergent in terms of overall quality. The results are presented below.

Poor Average Fair Good TotalBrand A 5 17 11 10 43Brand B 14 26 8 18 66Brand C 10 23 11 17 61Brand D 11 19 7 5 42Total 40 85 37 50 212

18. What percentage of the consumers found their detergent fair or good?

A) 0.49B) 0.41C) 0.39D) 0.29ANSWER: B

19. What percentage of the consumers evaluated product A?

A) 0.203B) 0.167C) 0.230D) None of the aboveANSWER: A

20. Of the customers who were given Brand A, what percentage rated it poor?

A) 0.125B) 0.024C) 0.116D) 0.189ANSWER: C

21. Which of the following is most likely a continuous numerical variable?

A) The number of gallons of paint purchased.B) The number of gallons of milk purchased.C) The population of Egypt in 2005.D) The number of miles of interstate highways.ANSWER: D

22. In rating the service provided by a waiter/waitress, the following responses are possible: excellent, above average, average, below average, and poor. The responses are coded from 1 to 5 with 5 being excellent. The scale of measurement these represent is:

A) nominalB) ordinalC) intervalD) ratioANSWER: B

16


23. An automobile insurance agent believes that company A is more reliable than company B. Which scale of measurement does this information represent?

A) NominalB) OrdinalC) IntervalD) RatioANSWER: B

24. Which of the following best describes the data: zip codes for students attending college in the state of California?

A) Qualitative dataB) Numerical dataC) Quantitative dataD) Time-series dataANSWER: A

25. Which of the following best describes the data: grade point averages for athletes?

A) Categorical dataB) Quantitative dataC) Qualitative dataD) Relative frequency dataANSWER: B

26. Consider the following data: like, no preference, or dislike. Which of the following best describes these data?

A) Qualitative dataB) Numerical dataC) Quantitative dataD) Attitude dataANSWER: A

27. At a large company, the majority of the employees earn from $20,000 to $30,000 per year. Middle management employees earn between $30,000 and $50,000 per year while top management earn between $50,000 and $100,000 per year. A histogram of all salaries would have which of the following shapes?

A) SymmetricalB) UniformC) Skewed to rightD) Skewed to leftANSWER: C

28. Which of the following statements is false?

A) Pareto diagram is a bar graph with the bars arranged from the most numerous categories to the least numerous categories.

B) Pareto diagram includes a line graph displaying the cumulative percentages and counts for the bars.

C) A Pareto diagram of types of defects will show the ones that have the greatest effect on the defective rate in order of effect. It is then easy to see which defects should be targeted in order to most effectively lower the defective rate.

D) None of the above.

17

Chapter 2

ANSWER: D29. Which of the following statements is false?

A) Relative frequencies are often useful in a presentation because nearly everybody understands fractional parts when expressed as percents.

B) Relative frequencies are particularly useful when comparing the frequency distributions of two different size sets of data.

C) The histogram of a sample should have a distribution shape that is skewed.D) A stem-and-leaf display contains all the information needed to create a histogram.ANSWER: C

30. Numerical variables can be subdivided into which two types?

A) Diverse and categoricalB) Discrete and continuousC) Nominal and progressiveD) Cross-sectional and discreteANSWER: B

31. Gender and State are examples of which type of data?

A) Discrete dataB) Continuous dataC) Categorical dataD) Ordinal dataANSWER: C

32. Which of the following is the graphical analog of a frequency table?

A) The histogramB) The scatterplotC) The time series plotD) The contingency tableANSWER: A

33. A variable is classified as ordinal if:

A) there is a natural ordering of categoriesB) there is no natural ordering of categoriesC) the data arise from continuous measurementsD) we track the variable through a period of timeANSWER: A

34. A time series plot is essentially a:

A) histogram.B) scatter plot.C) Pareto diagram.D) pie chart.ANSWER: B

18


True-False Questions

35. A histogram is the best graphical tool to display qualitative data. ANSWER: F

36. It is necessary for a discrete numerical variable to have a finite number of values.ANSWER: F

37. Ordinal data indicate the rank ordering of items, and similar to nominal data – the values are words that describe responses.ANSWER: T

38. An interval scale indicates rank and distance from a natural zero measured in unit intervals.ANSWER: F

39. Ratio scale data do indicate both rank and distance from a natural zero, with ratios of two measures having meaning.ANSWER: T

40. Bar charts and pie charts are commonly used to describe categorical data.ANSWER: T

41. A line chart is also called a time-series plot.ANSWER: T

42. A line chart is also called a scatter plot.ANSWER: F

43. An ogive is also called a cumulative line graph.ANSWER: T

44. Histograms may not be “mathematically correct” since they often cannot be scaled on the vertical axis.ANSWER: T

45. A stem-and-leaf displays an exploratory data analysis (EDA) graph that is an alternative to the line graph.ANSWER: F

46. In real life, there are not situations in which we need to describe relationships between categorical or ordinal variables.ANSWER: F

47. All graphic representations of sets of data need to be completely self-explanatory. That includes a descriptive meaningful title, and identification of the vertical and horizontal scales.ANSWER: T

48. The stem-and-leaf display for summarizing numerical data is a combination of a graphic technique and a sorting technique.ANSWER: T

19

Chapter 2

49. The histogram of a sample should have a distribution shape very similar to that of the population from which the sample was drawn. ANSWER: T

50. Cross tables have a stronger visual impact than graphs.ANSWER: F

51. One possible error in constructing a histogram is to make the heights of the rectangles, and not the areas of the rectangles, proportional to the frequencies.ANSWER: T

52. By selecting a particular scale of measurement, we can, in a time-series plot, create an impression either of relative stability or of substantial fluctuation over time.ANSWER: T

53. ATP singles rankings for tennis players is an example of an interval scale.ANSWER: F

54. Quantitative variables usually represent membership in groups or categories.ANSWER: F

55. When a variable is measured, a numerical value is assigned to it, and the result will be in one of four levels of measurement – nominal, ordinal, interval, or ratio.ANSWER: T

56. Every ogive starts on the left with a cumulative relative frequency of zero at the lower class boundary of the first class and ends on the right with a cumulative relative frequency of 100% at the upper class boundary of the last class. ANSWER: T

20


Basic and Applied Questions

QUESTIONS 57 AND 58 ARE BASED ON THE FOLLOWING INFORMATION:A recent study examined the intended travel destinations for a sample of residents from Grand Rapids, Michigan. The respondents indicated the likely destination of their next vacation. The results of this survey are as follows: 8% were contemplating an international trip, 16% were considering Florida, 30% said they would go to California, 36% thought they would go somewhere within Michigan, and the remaining 10% were looking at some other destination.

57. Construct a pie chart to show this information.

ANSWER:

58. Construct a bar chart to show this information

ANSWER:

21

Vacation Pie Chart

International8%

Florida16%

California30%

Michigan36%

Other10% International

Florida

California

Michigan

Other

Vacation Bar Chart

8

16

30

36

10

05

1015

2025

3035

40

International Florida California Michigan Other

Fre

qu

ecn

y

Chapter 2

QUESTIONS 59 THROUGH 63 ARE BASED ON THE FOLLOWING INFORMATION:The data presented below were collected on the amount of time it takes, in hours an employee, to process an order at a local plumbing wholesaler.

2.8 4.9 0.5 13.2 14.2 8.9 3.7 15.2 11.2 13.45.5 10.2 1.1 14.2 7.8 4.5 10.9 8.8 18.2 17.1

59. Construct a stem-and-leaf display of the data.

ANSWER:

60. Construct a frequency distribution of the data.

ANSWER:

22

Time(in hours) Frequency0 but < 3.5 3

3.5 but < 6.5 46.5 but < 9.5 39.5 but < 12.5 3

12.5 but < 15.5 515.5 but < 18.5 2

STEM LEAF UNIT = 0.1

0 51 12 83 74 5 95 567 88 8 99

10 2 911 21213 2 414 2 215 21617 118 2


61. Construct cumulative frequency and cumulative percentage distributions of the data.

ANSWER:

62. Use your answer to Question 60 to construct an appropriate histogram of the data.

ANSWER:

63. Determine the percentage of time it takes an employee at most 12.5 hours to process an order at the plumbing wholesaler.

ANSWER:65%

QUESTIONS 64 AND 65 ARE BASED ON THE FOLLOWING INFORMATION:An investment councilor recently reviewed the account activity of a sample of 10 of his clients and calculated the average number of stock trades per month over the past year for each client. He obtained the following data values: 10.2, 2.5, 11.4, 3.2, 1.1, 3.4, 8.4, 9.7, 11.2, and 2.4.


ANSWER:

23

Time (in hours Cumulative Frequency Cumulative %< 3.5 3 15%< 6.5 7 35%

< 9.5 10 50%

< 12.5 13 65%

< 15.5 18 90%

< 18.5 20 100%

Bins Frequency2.0 14.5 47.0 09.5 112.0 4

Histogram Chart of Process Times

0

1

2

3

4

5

6

3.5 6.5 9.5 12.5 15.5 18.5

Interval Times

Fre

qu

en

cy

Chapter 2

65. Use your answer to Question 64 to construct a histogram of the data

ANSWER:

66. The sales manager for a local commercial waste disposal company has tracked the yearly dollar value (in $1000) of contracts made by both internal sales people and external sales people. The data are presented below. Graph the data with a time plot. What possible conclusions or actions might the firm consider?

Year 1996 1997 1998 1999 2000 2001Internal Sales $357 375 412 368 345 333External Sales $672 680 695 721 730 734

ANSWER:

It appears that internal sales have been falling while external sales have been increasing slowly over the period.

24

Time Plot of Internal and External Sales

0

100

200

300

400

500

600

700

800

1999 2000 2001 2002 2003 2004

Year

Sal

es in

$10

00

Internal Sales

External Sales

Histogram of Investment Data

0

1

2

3

4

5

2.0 4.5 7.0 9.5 12.0

Bins

Fre

quen

cy


QUESTIONS 67 THROUGH 69 ARE BASED ON THE FOLLOWING INFORMATION:Data were collected on the number of people entering an electronics store each hour. The data are presented below.

23 35 42 28 29 17 38 21 49 5246 37 25 49 37 25 28 13 29 43

67. Construct a stem-and-leaf display of the data.

ANSWER:


ANSWER:

69. Construct cumulative frequency and cumulative percentage distributions of the data.

ANSWER:

25

Number of People Frequency10 but < 17 117 but < 24 324 but < 31 631 but < 38 338 but < 45 345 but < 52 352 but < 59 1

Number of people Cumulative Frequency Cumulative %10 but < 17 1 5%17 but < 24 4 20%

24 but < 31 10 50%

31 but < 38 13 65%

38 but < 45 16 80%

45 but < 52 19 95%

52 but < 59 20 100%

STEM LEAF UNIT = 1

1 3 72 1 3 5 5 8 8 9 93 5 7 7 84 2 3 6 9 95 2

Chapter 2

QUESTIONS 70 AND 71 ARE BASED ON THE FOLLOWING INFORMATION:The head of human resources at a large corporation was curious about levels of employment by classification. She determined that 12% of all employees were classified as executive, 13% as professional, 25% as clerical and janitorial, 32% as administrative and 18% as technical workers.

70. Construct a pie chart to show this information.

ANSWER:

71. Construct a bar chart to show this information.

ANSWER:

72. Briefly discuss the Pareto diagram.

ANSWER:A Pareto diagram, named after the Italian economist Vilfredo Pareto, is a bar chart that displays the frequency of defect causes. The bar at the left indicates the most frequent cause and bars to the right indicate causes with decreasing frequencies. A Pareto diagram is used to separate the “vital few” from the “trivial many”.

26

Level of Employment Bar Chart

1015

2530

20

05

101520253035

Exe

cutive

Pro

fessio

na

l

Cle

rical

Ad

min

istrative

Te

chn

ical

Fre

qu

en

cy

Level of Employment Pie Chart

Executive10%

Professional15%

Clerical25%

Administrative30%

Technical20%

Executive

Professional

Clerical

Administrative

Technical


73. A company has determined that there are seven possible defects for one of its product lines. Construct a Pareto diagram for the following defect frequencies:

ANSWER:

QUESTIONS 74 AND 75 ARE BASED ON THE FOLLOWING INFORMATION:The data in the next table indicate the number of degrees awarded from 1998 to 2005 by degree type at a four-year university in Illinois.

27

Defect Code FrequencyA 10B 70C 15D 90E 8F 4G 3

Year Bachelor Graduate Law1999 510 85 2232000 498 85 2632001 481 94 2702002 472 110 2702003 441 93 2522004 441 119 2822005 497 169 217

Count

Perc

ent

Defective CodeCount

35.0 7.5 5.0 4.0 3.5Cum % 45.0 80.0 87.5 92.5

90

96.5 100.0

70 15 10 8 7Percent 45.0

OtherEACBD

200

150

100

50

0

100

80

60

40

20

0

Pareto Chart of Defects

Chapter 2

74. Graph the data with a time-series plot.

ANSWER:

75. What possible conclusions or actions might the university consider?

ANSWER:The number of law and graduate degrees awarded is increasing. The number of bachelor degrees awarded declined from 1999 to 2004 with a slight increase in 2005. Enrollment restrictions may be in order if class sizes are becoming too large or if crowding conditions occur.

QUESTIONS 76 THROUGH 78 ARE BASED ON THE FOLLOWING INFORMATION:Percentage returns for the 25 largest U.S. common stock mutual funds for a particular day are displayed below.

24.3 13.6 19.7 25.0 31.0 21.8 24.9 31.5 20.2 25.933.2 28.3 20.6 39.8 30.6 19.0 20.6 37.1 24.8 29.931.1 32.6 49.9 31.1 38.3

76 Construct a histogram to describe the data.

28

Time series plot of degrees aw arded from 1999 to 2005

0

75

150

225

300

375

450

525

1999 2000 2001 2002 2003 2004 2005

Year

Nu

mb

er o

f d

egre

es

Bachelor

Graduate

Law


ANSWER:

77. Construct an ogive to describe the data.

ANSWER:

29

Histogram

0

2

4

6

8

10

15 20 25 30 35 40 45 50

Returns

Fre

qu

en

cy

Cumulative Percentage Ogive for Returns

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

15 20 25 30 35 40 45 50

Returns

Cu

mu

lati

ve P

erce

nta

ge

Chapter 2

78. Draw a stem-and-leaf display to describe the data.

ANSWER:

QUESTIONS 79 AND 80 ARE BASED ON THE FOLLOWING INFORMATION:The time (in hours) that a sample of 20 students studied for a statistics test are shown below

6.5 5.8 4.5 6.2 4.8 7.3 4.6 3.9 4.4 5.55.2 6.7 3.0 2.4 5.0 3.6 2.9 4.0 2.8 3.6

79. Construct a stem-and-leaf display for the data

ANSWER:

80. Describe graphically the time (in hours) that students studied for the test

ANSWER:

30

Stem-and-Leaf Display for Study Time

Stem unit: 1

2 4 8 93 0 6 6 94 0 4 5 6 85 0 2 5 86 2 5 77 3

Histogram

0

1

2

3

4

5

6

7

3 4.5 6 7.5

Time in hours

Fre

qu

en

cy

Stem-and-Leaf Display for returns

Stem unit: 10

1 4 92 0 0 1 1 2 4 5 5 5 6 83 0 1 1 1 1 2 3 3 7 84 05 0


QUESTIONS 81 AND 82 ARE BASED ON THE FOLLOWING INFORMATION:A statistics professor has developed the cross table presented below, that compares students’ class standing with their final grades.

Year A B C D F TotalFreshman 17 28 8 3 69Sophomore 14 23 17 10 1Junior 17 19 10 2 1 49Senior 5 8 4 0 17Total 67 59 20 5

81. Calculate the missing values identified by asterisks. What patterns do you see in this table?

ANSWER:

Year A B C D F TotalFreshman 13 17 28 8 3 69Sophomore 14 23 17 10 1 65Junior 17 19 10 2 1 49Senior 5 8 4 0 0 17Total 49 67 59 20 5 200

It appears that the earlier a student is in his or her college career, the worse they will do in class.

82. Convert the data to percentages. What patterns do you see in this table?

ANSWER:

Year A B C D F TotalFreshman 6.5% 8.5% 14.0% 4.0% 1.5% 34.5%Sophomore 7.0% 11.5% 8.5% 5.0% 0.5% 32.5%Junior 8.5% 9.5% 5.0% 1.0% 0.5% 24.5%Senior 2.5% 4.0% 2.0% 0.0% 0.0% 8.5%Total 24.5% 33.5% 29.5% 10% 2.5% 100%

The percentages of students failing the class for freshmen, sophomores, juniors, and seniors are 1.5%, 0.5%, 0.5% and 0.0%, respectively. It appears that the earlier a student is in his or her college career, the worse they will do in class.

83. In completing a survey, respondents use the following numbers to indicate marital status. 1 = Single (never married), 2 = Married,3 = Divorced,4 = WidowedIs this data qualitative or quantitative? Explain.

ANSWER:Even though marital status is coded by number, the data is qualitative as it categorizes each individual respondent. Also, the average of single and divorced is meaningless.

31

Chapter 2

84. A consumer goods company has been studying the effect of advertising on total profits. As part of this study, data on advertising expenditures ($1000s) and total sales ($1000s) were collected for a five-month period and are as follows: (15, 150), (22.5, 300), (10.5, 120), (18, 180), and (21, 225), where the first number is advertising expenditures and the second is total sales. Graphically display the data, and state any conclusion that you might draw from the graph.

ANSWER:

Clearly the is a positive relationship between advertising expenditures and total sales.

85. In completing a survey, respondents use the following numbers to indicate ages. 1 = Age 19 years and under,2 = 20 to 29 years of age3 = 30 to 39 years of age,4 = Age 40 years and olderIs this data qualitative or quantitative? Explain.

ANSWER:This is quantitative data; an average age.

86. Explain the difference between the terms “variable” and “data.” Include an illustration that demonstrates this difference.

ANSWER:Variable: a characteristic of interest about each individual element of a population or a sampleData: refer to the value or values of the variable of interestIllustration: The age of a person when first attends professional sporting event would be characteristic of interest about each person and is a variable. Jim was 17 when he first attended a professional sporting event; 17 is the value of the variable for Jim and is data).

87. A department of mathematical sciences has majors in four areas.

32

Scatter Plot

0

50

100

150

200

250

300

350

5 10 15 20 25

Advertising Expenditures

To

tal

Sa

les


Major Number of MajorsMathematics 50Computer Science 22Actuarial Science 15Statistics 10

If a circle graph is constructed for these data, what would be the percentage of the graph for each major?

ANSWER:

Major % of MajorsMathematics 51.5Computer Science 22.7Actuarial Science 15.5Statistics 10.3

QUESTIONS 88 THROUGH 91 ARE BASED ON THE FOLLOWING INFORMATION:The final-inspection defect report for an assembly line is reported on the table and Pareto diagram as shown below:

Defect Blemish Scratch Chip Bend Dent OthersCount 61 50 28 17 13 11

88. What is the total defect count in the report?

ANSWER:180 defects

89. Find the percentage for “chip” defect items.

ANSWER:Percent of chip = (50/180) 100% = 15.56%

33

Chapter 2

90. Find the cumulative % for bend, and explain what that value means.

ANSWER:[(61+50+28+17) /180] 100% = (156/180) 100% = 86.67%. The value 86.67% is the sum of the percentages for all defects that occurred more often than Bend, including Bend.

91. Management has given the production line the goal of reducing their defects by 50%. What two defects would you suggest they give special attention to in working toward this goal? Explain.

ANSWER:The two defects, Blemish and Scratch, total 61.67%. If they can control these two defects, the goal should be within reach.

QUESTIONS 92 THROUGH 94 ARE BASED ON THE FOLLOWING INFORMATION:What not to get them on Valentines Day! A recent study among adults in USA shows that adults prefer not to receive certain items as gifts on Valentine’s Day; namely, Teddy bears: 45%; Chocolate: 25%; Jewelry: 15%; Flowers: 12%; Don’t Know: 3%.

92. Draw a Pareto diagram picturing the “Presents not wanted”.

ANSWER:

93. If you want to be 80% sure you did not get your valentine something unwanted, what should you avoid buying? How does the Pareto diagram show this?

ANSWER:Teddy bears, chocolates, jewelry; these are listed first in the Pareto diagram.

94. 400 adults are to be surveyed, what frequencies would you expect to occur for each unwanted item listed on the snapshot?

ANSWER:The frequencies are 180, 100, 60, 48, and 12 for teddy bears, chocolates, jewelry, flowers, and don’t know, respectively.

34

Count

Perc

ent

Unwanted PresensCount

15.0 12.0 3.0Cum % 45.0 70.0 85.0 97.0 100.0

45 25 15 12 3Percent 45.0 25.0

OtherFlowersJ ewelryChocolateTeddy Bears

100

80

60

40

20

0

100

80

60

40

20

0

Pareto Diagram for Unwanted Presents


95. The students at small community college in Iowa apply to study either English or Business. Some administrators at the college are concerned that women are being discriminated against in being allowed admittance, particularly in the business program. Below, you will find two contingency tables that show the percentage of students admitted by gender to the English program and the Business school. The data has also been presented graphically. What do the data and graphs indicate?

English programGender No Yes TotalFemale 46.0% 54.0% 100%Male 60.8% 39.2% 100%Total 53.5% 46.5% 100%

Business schoolGender No Yes TotalFemale 69.2% 30.8% 100%Male 64.1% 35.9% 100%Total 65.4% 34.6% 100%

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ANSWER:These data indicate that a smaller percentage of women are being admitted to the business program. Only 30.8% of women are being admitted to the business program compared to 35.9% for men. However, it is also important to note that only 34.6% of all applicants (women and men) are admitted to the business program compared to 46.5% for the English program. Maybe the males should say something about being discriminated against in being admitted to the English program.

QUESTIONS 96 THROUGH 105 ARE BASED ON THE FOLLOWING INFORMATION:A sample of 150 students at a State University was taken after the final business statistics exam to ask them whether they went partying the weekend before the final or spent the weekend studying, and whether they did well or poorly on the final. The following table contains the result.

Did Well in Exam Did Poorly in ExamStudying for Exam 60 15Went Partying 22 53

96. Of those in the sample who went partying the weekend before the final exam, what percentage of them did well in the exam?

ANSWER:22 out of 75, or 29.33%

97. Of those in the sample who did well on the final exam, what percentage of them went partying the weekend before the exam?


98. What percentage of the students in the sample went partying the weekend before the final exam and did well in the exam?


99. What percentage of the students in the sample spent the weekend studying and did well in the final exam?

ANSWER:60 out of 150, or 40%

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100. What percentage of the students in the sample went partying the weekend before the final exam and did poorly on the exam?


101. If the sample is a good representation of the population, what percentage of the students in the population should we expect to spend the weekend studying and do poorly on the final exam?


102. If the sample is a good representation of the population, what percentage of those who spent the weekend studying should we expect to do poorly on the final exam?


103. If the sample is a good representation of the population, what percentage of those who did poorly on the final exam should we expect to have spent the weekend studying?


104. Of those in the sample who went partying the weekend before the final exam, what percentage of them did poorly in the exam?


105. Of those in the sample who did well in the final exam, what percentage of them spent the weekend before the exam studying?


106. The data in the time series plot below represents monthly sales for two years of beanbag animals at a local retail store (Month 1 represents January and Month 12 represents December). Do you see any obvious patterns in the data? Explain.

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Chapter 2

ANSWER:This is a representation of seasonal data. There seems to be a small increase in months 3, 4, and 5 and a large increase at the end of the year. The sales of this item seem to peak in December and have a significant drop off in January.

107. The 2005 mobile phone manufacturers' global market shares were as follows: Nokia 26.9%, Motorola 16.9%, Ericson 10.5%, Samsung 6.2%, Panasonic 5.5%, others (Siemens, Alcatel, Mitsubishi, Philips, NEC, and more) 34.0%. Present this information in a pie chart.

ANSWER:

108. Create a time-series line graph showing U.S. federal government deficits (-) or surpluses (+) for 1975-1999 (in billions of dollars):

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-69.3 -53.0 -45.1 -26.9 -11.3 -53.8 -53.7 -132.6 -173.9 -168.0 -177.2 -192.1 -147.9 -137.3 -130.0 -173.0 -215.3 -297.6 -274.2 -212.3 -192.0 -136.8 -53.3 +49.0 +124.4

ANSWER:

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Ch 2