Describing Data: Graphical · 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

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11

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 ratio B) Ordinal, nominal, interval and ratio C) Interval, nominal, ratio and ordinal D) Nominal, interval, ordinal, and ratio

ANSWER: 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

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12

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) 3 B) 15 C) 16 D) 25

ANSWER: B


10 1 5.00%

15 9 50.00%

20 1 55.00%

25 7 90.00%

More 2 100.00%


12.8 1 5.00%

41.6 5 30.00%

70.4 6 60.00%

99.2 6 *

More 2 100.00%

Full file at https://fratstock.euDescribing Data: Graphical

13

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-leaf Dollars N = 25 Leaf Unit = 10.0 2 2 5 7 (7) 3 1 1 4 5 6 7 8 5 4 2 2 4 5 9 1 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-leaf Dollars N = 30 Leaf Unit = 10.0

2 5 0 4 8 5 6 0 0 2 4 5 9 (11) 7 0 0 2 2 3 3 5 5 7 7 8 6 8 0 0 2 3 7 8 3 9 2 2 7 1 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) nominal B) ordinal C) interval D) ratio

ANSWER: A


14

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


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” Rule B) “80-20” Rule C) “10-90” Rule D) “90-10” Rule ANSWER: B

25%

17%39%

12%7% Friend

Magazine

TV

Internet

Other


15

QUESTIONS 14 THROUGH 17 ARE BASED ON THE FOLLOWING INFORMATION: 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) 0.620 B) 0.305 C) 0.510 D) 0.543

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

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

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

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

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

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

ANSWER: D

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


16

QUESTIONS 18 THROUGH 20 ARE BASED ON THE FOLLOWING INFORMATION: 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 Total

Brand A 5 17 11 10 43

Brand B 14 26 8 18 66

Brand C 10 23 11 17 61

Brand D 11 19 7 5 42

Total 40 85 37 50 212

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

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

ANSWER: B 19. What percentage of the consumers evaluated product A?

A) 0.203 B) 0.167 C) 0.230 D) None of the above

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

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

ANSWER: 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) nominal B) ordinal C) interval D) ratio

ANSWER: B


17

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

A) Nominal B) Ordinal C) Interval D) Ratio ANSWER: B

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

A) Qualitative data B) Numerical data C) Quantitative data D) Time-series data

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

A) Categorical data B) Quantitative data C) Qualitative data D) Relative frequency data

ANSWER: B 26. Consider the following data: like, no preference, or dislike. Which of the following best

describes these data?

A) Qualitative data B) Numerical data C) Quantitative data D) Attitude data

ANSWER: 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) Symmetrical B) Uniform C) Skewed to right D) Skewed to left

ANSWER: 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. ANSWER: D


18

29. 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 categorical B) Discrete and continuous C) Nominal and progressive D) Cross-sectional and discrete ANSWER: B

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

A) Discrete data B) Continuous data C) Categorical data D) Ordinal data ANSWER: C

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

A) The histogram B) The scatterplot C) The time series plot D) The contingency table ANSWER: A

33. A variable is classified as ordinal if:

A) there is a natural ordering of categories B) there is no natural ordering of categories C) the data arise from continuous measurements D) we track the variable through a period of time ANSWER: A

34. A time series plot is essentially a:

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


19

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


20

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


21

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:

Vacation Pie Chart

International

8%

Florida

16%

California

30%

Michigan

36%

Other

10% International

Florida

California

Michigan

Other

Vacation Bar Chart

8

16

30

36

10

0

5

10

15

20

25

30

35

40

International Florida California Michigan Other

Fre

qu

ecn

y


22

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 13.4 5.5 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:

Time(in hours) Frequency

0 but < 3.5 3

3.5 but < 6.5 4

6.5 but < 9.5 3

9.5 but < 12.5 3

12.5 but < 15.5 5

15.5 but < 18.5 2

STEM LEAF UNIT = 0.1

0 5

1 1

2 8

3 7

4 5 9

5 5

6

7 8

8 8 9

9

10 2 9

11 2

12

13 2 4

14 2 2

15 2

16

17 1

18 2


23

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. 64. Construct a frequency distribution of the data.

ANSWER:

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 Frequency

2.0 1

4.5 4

7.0 0

9.5 1

12.0 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


24

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 2001

Internal Sales $357 375 412 368 345 333

External 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.

Time Plot of Internal and External Sales

0

100

200

300

400

500

600

700

800

1999 2000 2001 2002 2003 2004

Year

Sa

les

in

$1

00

0

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

quency


25

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 52 46 37 25 49 37 25 28 13 29 43 67. Construct a stem-and-leaf display of the data.

ANSWER: 68. Construct a frequency distribution of the data.

ANSWER:

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

ANSWER:

Number of People Frequency

10 but < 17 1

17 but < 24 3

24 but < 31 6

31 but < 38 3

38 but < 45 3

45 but < 52 3

52 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 7

2 1 3 5 5 8 8 9 9

3 5 7 7 8

4 2 3 6 9 9

5 2


26

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”.

Level of Employment Bar Chart

10

15

25

30

20

0

5

10

1520

25

30

35

Exe

cu

tive

Pro

fessio

na

l

Cle

rica

l

Ad

min

istra

tive

Te

ch

nic

al

Fre

qu

en

cy

Level of Employment Pie Chart

Executive

10%

Professional

15%

Clerical

25%

Administrative

30%

Technical

20%Executive

Professional

Clerical

Administrative

Technical


27

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.

Defect Code Frequency

A 10 B 70 C 15 D 90 E 8 F 4 G 3

Year Bachelor Graduate Law

1999 510 85 223 2000 498 85 263 2001 481 94 270 2002 472 110 270 2003 441 93 252 2004 441 119 282 2005 497 169 217

Count

Perc

ent

Defective CodeCount

35.0 7.5 5.0 4.0 3.5

Cum % 45.0 80.0 87.5 92.5

90

96.5 100.0

70 15 10 8 7

Percent 45.0

OtherEACBD

200

150

100

50

0

100

80

60

40

20

0

Pareto Chart of Defects


28

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 25.9 33.2 28.3 20.6 39.8 30.6 19.0 20.6 37.1 24.8 29.9 31.1 32.6 49.9 31.1 38.3

Time series plot of degrees awarded from 1999 to 2005

0

75

150

225

300

375

450

525

1999 2000 2001 2002 2003 2004 2005

Year

Nu

mb

er

of

deg

rees

Bachelor

Graduate

Law


29

76 Construct a histogram to describe the data. ANSWER: 77. Construct an ogive to describe the data. ANSWER:

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

erc

en

tag

e


30

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 5.5 5.2 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:

Stem-and-Leaf Display for Study Time

Stem unit: 1

2 4 8 9

3 0 6 6 9

4 0 4 5 6 8

5 0 2 5 8

6 2 5 7

7 3

Histogram

0

1

2

3

4

5

6

7

3 4.5 6 7.5

Time in hours

Fre

qu

ency

Stem-and-Leaf Display for returns

Stem unit: 10

1 4 9

2 0 0 1 1 2 4 5 5 5 6 8

3 0 1 1 1 1 2 3 3 7 8

4 0

5 0


31

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 Total

Freshman 17 28 8 3 69 Sophomore 14 23 17 10 1 Junior 17 19 10 2 1 49 Senior 5 8 4 0 17

Total 67 59 20 5

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

table? ANSWER:


Freshman 13 17 28 8 3 69 Sophomore 14 23 17 10 1 65 Junior 17 19 10 2 1 49 Senior 5 8 4 0 0 17

Total 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:


Freshman 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 = Widowed

Is 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.


32

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 age 3 = 30 to 39 years of age, 4 = Age 40 years and older Is 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 sample Data: refer to the value or values of the variable of interest Illustration: 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).

Scatter Plot

0

50

100

150

200

250

300

350

5 10 15 20 25

Advertising Expenditures

To

tal

Sal

es


33

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

Major Number of Majors

Mathematics 50 Computer Science 22 Actuarial Science 15 Statistics 10

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

for each major?

ANSWER:

Major % of Majors

Mathematics 51.5 Computer Science 22.7 Actuarial Science 15.5 Statistics 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 Others

Count 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%

Pareto Chart for Product Defects

0

60

120

180

Blem Scratch Chip Bend Dent Others

Defect type

Co

un

t

0

0.2

0.4

0.6

0.8

1

Perc

en

t


34

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.

Count

Perc

ent

Unwanted PresensCount

15.0 12.0 3.0

Cum % 45.0 70.0 85.0 97.0 100.0

45 25 15 12 3

Percent 45.0 25.0

OtherFlowersJewelryChocolateTeddy Bears

100

80

60

40

20

0

100

80

60

40

20

0

Pareto Diagram for Unwanted Presents


35

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 program

Gender No Yes Total

Female 46.0% 54.0% 100% Male 60.8% 39.2% 100%

Total 53.5% 46.5% 100%

Business school

Gender No Yes Total

Female 69.2% 30.8% 100% Male 64.1% 35.9% 100%

Total 65.4% 34.6% 100%

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 Exam

Studying for Exam 60 15

Went 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?

ANSWER: 22 out of 82, or 26.83%

0.0%

20.0%

40.0%

60.0%

80.0%

No YesFem

ale

Male

Percent Admitted by Gender

Female

Male

No YesFem

ale

Male

0.0%

20.0%

40.0%

60.0%

80.0%

Percent of Business Students

Admitted

Female

Male


36

98. What percentage of the students in the sample went partying the weekend before the

final exam and did well in the exam?

ANSWER: 22 out of 150, or 14.67% 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% 100. What percentage of the students in the sample went partying the weekend before the

final exam and did poorly on the exam?

ANSWER: 53 out of 150, or 35.33% 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?

ANSWER:

15 out of 150, or 10% 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?

ANSWER: 15 out of 75, or 20% 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?

ANSWER: 15 out of 68, or 22.06% 104. Of those in the sample who went partying the weekend before the final exam, what

percentage of them did poorly in the exam?

ANSWER: 53 out of 75, or 70.67% 105. Of those in the sample who did well in the final exam, what percentage of them spent the

weekend before the exam studying?

ANSWER: 60 out of 82, or 73.17%


37

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.

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:

Nokia

27%

Motorola

17%

Ericson

11%

Samsung

6%

Panasonic

6%

Others

33%

Time series chart of Sales

75

150

225

300

375

450

525

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Observation Number

Sale

s


38

108. Create a time-series line graph showing U.S. federal government deficits (-) or surpluses

(+) for 1975-1999 (in billions of dollars):

-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:

-350

-300

-250

-200

-150

-100

-50

0

50

100

150

1975 1980 1985 1990 1995 2000

Documents

Describing Data: Graphical · 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