Ch 2

CHAPTER 2 Describing Data: Graphical  Multiple-Choice Questions 1.

Which Which of the following following variables variables is an example example of a categorica categoricall variable? variable? A) B) C) D)

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

ANSWER:

2.

C

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

3.

B

What What is is the the correc correctt ranki ranking ng of data data from from weak weakest est or lowe lowest st type type to stro stronges ngestt or higher  higher  type? A) Nominal, ordinal, interval and ratio ratio B) Ordinal, nominal, interval and ratio ratio C) Interval, nominal, ratio and ordinal ordinal D) Nominal, interval, ordinal, and ratio ANSWER:

4.

A

Which Which of the follow following ing statem statement ents s is incorr incorrect ect? ? A) B) C) D)

Ordinal data may be described described as qualitative. Nominal data may be described described as quantitative. A categorical variable may produce ordinal data. A discrete numerical numerical variable variable may produce ratio scale data. data.

ANSWER:

B

11

Chapter 2

5.

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

Freq Freque uenc ncy y Cumu Cumula lati tive ve %

10 15 20 25 More

1 9 1 7 2

5.00% 50.00% 55.00% 90.00% 100.00%

Which of the following statements is true? A) It took 50% of all workers workers exactly 15 minutes to assemble the 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:

6.

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

Freq Freque uenc ncy y Cumu Cumula lati tive ve %

12.8 41.6 70.4 99.2 More A) B) C) D)

5.00% 30.00% 60.00% * 100.00%

D

Consid Consider er the follow following ing frequen frequency cy distri distribut bution ion genera generated ted by Excel. Excel. What What is is the the missi missing ng frequency value identified by asterisk?

A) B) C) D)

Bin Bin

Freque equenc ncy y

Cumul umulat atiive %

584 1774.4 2964.8 4155.2 5345.6 More

1 * 4 3 1 1

4.00% 64.00% 80.00% 92.00% 96.00% 100.00%

3 15 16 25

ANSWER:

12

1 5 6 6 2

60.0 60.00% 0% 5.00 5.00% % 100% 100% 90% 90%

ANSWER:

7.

C

B

Describing Data: Graphical

8.

Data Data on the monthl monthly y expen expenses ses (in (in $) submi submitte tted d by 15 peop people le on on a firm firm’s ’s sale sales s staff staff are summarized in the following stem-and-leaf display. Stem-and-leaf  Dollars N = 25 Leaf Unit = 10.0 2 2 57 (7) 3 1145678 5 4 22459 1 5 1 Which of the following statements is not n ot true? A) The leaf leaf 7 represents represents $70. B) The number 5 in the left-hand column column tells us that five people had expenses 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:

9.

C

A samp sample le of 30 30 profes professio sional nal men was asked asked to to estim estimate ate their their yearly yearly expendi expenditur tures es on on clothes for work. The data are summarized in the following following stem-and-leaf display. Stem-and-leaf  Dollars N = 30 Leaf Unit = 10.0 5 048 2 5 6 002459 (11) 7 0 0 2 2 3 3 5 5 7 7 8 6 8 002378 3 9 227 10 0 1 What percentage of these men spent more than $900 on professional attire? A) 87.7 87.7% % B) 13.3 13.3% % C) 16.7% D) 83.3% ANSWER:

10.

B

Profe Professo ssorr Ander Anderson son grad graduat uated ed from from the the Univer Universit sity y of Michi Michigan gan wit with h a code valu value e = 1 while Professor Jackson graduated from Michigan State with a code value = 2. The scale of measurement likely represented by this information is: A) B) C) D)

nomi nomina nall ordi ordina nall inte interv rval al rati atio

ANSWER:

A

13

Chapter 2

11.

Consid Consider er the the follow following ing freq frequen uency cy distr distribu ibuti tion on gener generate ated d by Exce Excel. l. What What propor proportio tion n of  these values are less than 63? Bin Bin

Freq requenc uency y

Cumul umulat ativ ive e%

26 44.5 63 81.5 More

0 5 7 1 7

0.00% 25.00% 60.00% 65.00% 100.00%

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

12.

A

Companies Companies are often often interes interested ted in knowing knowing how how customers customers learned learned about about their products. 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.

7%

12%

25%

Friend Magazine TV

17%

39%

Internet Other 

What percentage of respondents learned about the product through television or the Internet? A) B) C) D)

12% 12% 39% 39% 51% 51% 100% 100%

ANSWER:

13. 13.

Pare Pareto to’s ’s resu result lt is appli applied ed to a wide wide varie variety ty of behav behavio iorr over many many syste systems ms.. It is sometimes referred to as the A) B) C) D)

“20-80” “20-80” Rule “80-20” “80-20” Rule “10-90” “10-90” Rule “90-10” “90-10” Rule

ANSWER:

14

C

B

Describing Data: Graphical

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:

Northeast South Midwest West Column Total

14.

Single Male 12 31

Single Female 17 26

Married Male 22 8

Married Female 10 23

Row Total

45 34

33 19

52 24

38 13

168 90

122

95

99

84

400

61 88

What percentage percentage of the respondents respondents were unmarried unmarried people? people? A) 0.620

B) 0.30 0.305 5 C) 0.510 D) 0.543 ANSWER:

15.

D

What percentage percentage of the respondents respondents were unmarried unmarried people from the Midwest? Midwest? A) 0.19 0.195 5 B) 0.543 C) 0.464 D) 0.359 ANSWER:

16.

What percentage percentage of the respondents respondents were single single people people from the Northeast? Northeast? A) B) C) D)

0.543 0.073 0.475 0.134

ANSWER:

17.

A

B

What percentage percentage of the respondents respondents were married married people people from the South? South? A) 0.114 B) 0.169 C) 0.352

D) 0.07 0.078 8

15

Chapter 2 ANSWER:

D

QUESTIONS 18 THROUGH 20 ARE BASED ON THE FOLLOWING INFORMATION:

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

Average

Fair

Good

Total

Brand C 

5 14 10

17 26 23

11 8 11

10 18 17

43 66 61

Brand D

11

19

7

5

42

Total

40

85

37

50

212

Brand A Brand B

18.

What percentage percentage of the consumers consumers found their detergent detergent fair or good? A) B) C) D)

0.49 0.41 0.39 0.29

ANSWER:

19.

B

What percentage percentage of the consumers consumers evaluated evaluated product product A? A) 0.203 B) 0.167 C) 0.230

D) None of the above ANSWER:

20.

A

Of the custom customers ers who were were given given Brand Brand A, what percentage rated it poor? A) 0.125 B) 0.024

C) 0.11 0.116 6 D) 0.189 ANSWER:

21.

Which Which of the following following is most likely likely a continuous continuous numerical numerical variable? variable? A) B) C) D)

The number of gallo gallons ns of of paint paint purchased. purchased. The number of gallo gallons ns of of milk milk purcha purchased. sed. The population population of Egypt in 2005. The number of miles miles of inters interstate tate highways. highways.

ANSWER:

16

C

D

Describing Data: Graphical 22.

In rating rating the servic service e provided provided by a waiter/w waiter/waitre aitress, ss, the followin following g responses responses are possible: 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) B) C) D)

nomi nomina nall ordi ordina nall inte interv rval al rati atio

ANSWER:

23.

An automo automobil bile e insura insurance nce agent agent belie believes ves that that compan company y A is more reliable than company B. Which scale of measurement does this information represent? A) B) C) D)

Nomi Nomina nall Ordi Ordina nall Inte Interv rval al Rati atio

ANSWER:

24.

Qualitativ Qualitative e data Numerical Numerical data Quantitati Quantitative ve data Time-seri Time-series es data

ANSWER:

A

Which Which of the following following best describes describes the data: grade point averages averages for athletes? athletes? A) B) C) D)

Categorica Categoricall data Quantitati Quantitative ve data Qualitativ Qualitative e data Relative Relative frequency frequency data

ANSWER:

26.

B

Which Which of the followin following g best best describe describes s the the data: data: zip zip codes codes for students students attendi attending ng colleg college e in the state of California? A) B) C) D)

25.

B

B

Consider Consider the following following data: like, no preference preference,, or or dislike. dislike. Which of the followin following g best best describes these data? A) B) C) D)

Qualitativ Qualitative e data Numerical Numerical data Quantitati Quantitative ve data Attitude Attitude data

ANSWER:

A

27.

At a larg large e compan company, y, the the majori majority ty of the the emplo employee yees s earn earn from from $20,00 $20,000 0 to $30,0 $30,000 00 per  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) Unifor Uniform m C) Skewed Skewed to right D) Skewed Skewed to left ANSWER:

C

17

Chapter 2 28.

Which Which of the follow following ing statem statement ents s is false? false? A) Pareto Pareto diagram diagram is a bar graph graph with with the bars arrange arranged d from from the most numerous numerous categories to the least numerous categories. B) Pareto Pareto diagram includes a line graph displaying displaying the cumulativ cumulative e percentages percentages and counts for the bars. C) A Pareto diagram of types types of defects will show the 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. above. ANSWER:

29.

D

Which Which of the follow following ing statem statement ents s is false? false? A) Relative Relative frequencies frequencies are often useful in a presentati presentation on because nearly everybody 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 distribution shape that is skewed. D) A stem-and-leaf display display contains all the the information needed to to create a histogram. ANSWER:

30.

Numerical Numerical variables variables can be subdivided subdivided into which which two types? types? A) B) C) D)

Diverse Diverse and categorica categoricall Discrete Discrete and continuous continuous Nominal Nominal and progressiv progressive e Cross-sect Cross-sectional ional and discrete discrete

ANSWER:

31.

Discr Discrete ete data data Contin Continuou uous s data data Categor Categorica icall data data Ordina Ordinall data data

ANSWER:

The histog histogram ram The scatte scatterpl rplot ot The time series series plot The contingency contingency table table

ANSWER:

there is a natural natural ordering ordering of catego categories ries there is no natura naturall orderi ordering ng of categories categories the data data arise arise from continuous continuous measureme measurements nts we track the variable through a period of time

ANSWER:

A

A time time series series plot plot is essent essential ially ly a: A) histogram.

18

A

A variab variable le is class classifi ified ed as ordin ordinal al if: A) B) C) D)

34.

C

Which Which of the following following is the graphical graphical analog analog of a frequency frequency table? table? A) B) C) D)

33.

B

Gender Gender and State are examples examples of which type of data? A) B) C) D)

32.

C

Describing Data: Graphical B) scatter plot. C) Pareto diagram. D) pie chart. ANSWER:

B

19

Chapter 2

True-False Questions 35.

A histogram histogram is the best graphical graphical tool to display display qualitativ qualitative e data. ANSWER:

36.

It is necessary necessary for a discre discrete te numeri numerical cal variable variable to have a finit finite e number number of values. values. ANSWER:

37.

T

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

20

F

All graphic graphic represe representati ntations ons of of sets sets of data need to be be complet completely ely self-expla self-explanator natory. y. That That includes a descriptive meaningful title, and identification of the vertical and horizontal scales. ANSWER:

48.

F

In real real life, life, there there are not situation situations s in which we need need to describe describe relationsh relationships ips betwe between en categorical or ordinal variables. ANSWER:

47.

T

A stem-a stem-and-le nd-leaf af display displays s an exploratory exploratory data analysis analysis (EDA) (EDA) graph graph that that is is an alternativ alternative e to the line graph. ANSWER:

46.

T

Histogram Histograms s may may not not be “mathemati “mathematicall cally y correct” correct” since since they they often often cannot cannot be scaled scaled on the the vertical axis. ANSWER:

45.

F

An ogive is also called called a cumulativ cumulative e line graph. graph. ANSWER:

44.

T

A line line chart chart is also also called called a scatte scatterr plot. plot. ANSWER:

43.

T

A line chart is also called called a time-ser time-series ies plot. ANSWER:

42.

T

Bar charts charts and pie charts charts are commonly commonly used to describe describe categorica categoricall data. ANSWER:

41.

F

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

40.

T

An inter interva vall scale scale indi indica cate tes s rank and and dist distan ance ce from from a natu natura rall zero meas measur ured ed in unit intervals. ANSWER:

39.

F

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

38. 38.

F

T

Describing Data: Graphical 49.

The hist histogr ogram am of a samp sample le shoul should d have have a distri distribut bution ion shap shape e very very simila similarr to that that of of the population from which the sample was drawn. ANSWER:

50.

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

51.

F

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

56.

F

Quantitat Quantitative ive variables variables usually usually represent represent membership membership in groups or categories categories.. ANSWER:

55.

T

ATP singles singles rankings rankings for tennis tennis player players s is is an an example example of an interval interval scale. scale. ANSWER:

54.

T

By select selecting ing a particul particular ar scale scale of measur measurement ement,, we we can, can, in in a time-seri time-series es plot, plot, create create an impression either of relative stability or of substantial fluctuation over time. ANSWER:

53.

F

One possible possible error error in constr constructi ucting ng a histogram histogram is to to make make the the heights heights of the the rectan rectangles, gles, and not the areas of the rectangles, proportional to the frequencies. ANSWER:

52.

T

T

Every Every ogive ogive star starts ts on the the left left with with a cumula cumulativ tive e relati relative ve frequ frequenc ency y of zero zero at the the lower  lower  class class bounda boundary ry of the first first class class and ends on the right with a cumula cumulativ tive e relati relative ve frequency of 100% at the upper class boundary of the last class. ANSWER:

T

21

Chapter 2

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. Michigan. The respondents indicated the the likely destination of their next vacation. vacation. The results of this survey are as follows: 8% were contemplating an international trip, 16% were cons consid ider erin ing g Flor Florid ida, a, 30% 30% said said they they woul would d go to Cali Califo forn rnia ia,, 36% 36% thou though ghtt they they woul would d go somewhere within Michigan, and the remaining 10% were looking at some other destination. 57.

Construct Construct a pie chart to show this informati information. on. ANSWER:

Vacation Pie Chart International 8%

Other  10%

International

Florida 16%

Florida California

Michigan 36%

Michigan California 30%

58.

Other 

Construct Construct a bar chart to show this informati information on ANSWER:

Vacation Bar Chart 36

40

y n c e u q e r F

35 30

30

25 20 15 10 5 0

16

In te tern at ati on on al al

22

10

8

Fl or ori da da

C al al ififo rn rn ia ia

Mi ch ch ig ig an an

Oth er er  

Describing Data: Graphical 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 5.5

4.9 10.2

0.5 1.1

13.2 14.2

14.2 7.8

8.9 4.5

3.7 10.9

59.

Construct Construct a stem-and-l stem-and-leaf eaf display display of the data.

15.2 8.8

11.2 18.2

13.4 17.1

ANSWER:

ST 1 60.

Construct Construct a frequency frequency distributi distribution on of the data. ANSWER:

Time( Time(in in hours) hours)

Freque Frequency  ncy 

0 but < 3.5 3.5 but < 6.5 6.5 but < 9.5 9.5 but < 12.5 12.5 but < 15.5 15.5 but < 18.5

3 4 3 3 5 2

4

59 23

Chapter 2 61.

Construct Construct cumulative cumulative frequency frequency and cumulative cumulative percentage percentage distributi distributions ons of the data. ANSWER:

62.

Time Time (in (in hour hours s

Cumu Cumula lati tive ve Freq Freque uency  ncy 

Cumulative %

< 3.5 < 6.5 < 9.5 < 12.5 < 15.5 < 18.5

3 7 10 13 18 20

15% 35% 50% 65% 90% 100%

Use your answer answer to to Questi Question on 60 to to constr construct uct an appropriat appropriate e histogr histogram am of the data. ANSWER:

Histogram Chart of Process Times 6 5 y 4 c n e u3 q e r 2 F

1 0 3 .5

6 .5

9.5

1 2.5

15 .5

18 .5

Interval Times

63.

Determin Determine e the percentage percentage of time time it takes an employe employee e at most 12.5 hours to proces process s 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 stock trades per month over the 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 Construct a frequency frequency distributi distribution on of the data. ANSWER:

24

Bins ins

Frequ requen ency  cy 

2.0 4.5 7.0 9.5 12.0

1 4 0 1 4

Describing Data: Graphical 65.

Use your your answer answer to Questi Question on 64 to construct a histogram of the data ANSWER: Histogram of Investment Data 5 4 y c n3 e u q e2 r F

1 0 2 .0

4 .5

7.0

9 .5

12 .0

Bins

66.

The sale sales s manage managerr for a local local comm commerc ercial ial wast waste e dispos disposal al compa company ny has tra tracke cked d 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 Internal Sales External Sales

1996 $357 $672

1997 375 680

1998 412 695

1999 368 721

2000 345 730

2001 333 734

ANSWER:

8 00 It appears that internal sales have been falling while external sales have been increasing slowly over the period.

25

Chapter 2 QUESTIONS 67 THROUGH 69 ARE BASED ON THE FOLLOWING INFORMATION:

Data were collected on the number of people entering entering an electronics store each hour. The data are presented below. 23 46

35 37

42 25

28 49

29 37

17 25

38 28

67.

Construct Construct a stem-and-l stem-and-leaf eaf display display of the data.

21 13

49 29

52 43

ANSWER:

ST 68.

Construct Construct a frequency frequency distributi distribution on of the data. ANSWER:

69.

Numb Number er of Peopl eople e

Freq Freque uenc ncy  y 

10 but < 17 17 but < 24 24 but < 31 31 but < 38 38 but < 45 45 but < 52 52 but < 59

1 3 6 3 3 3 1

Construct Construct cumulative cumulative frequency frequency and cumulative cumulative percentage percentage distributi distributions ons of the data. ANSWER:

Numb Number er of peop people le

Cumu Cumula lati tive ve Freq Freque uency  ncy 

Cumulative %

10 but < 17 17 but < 24 24 but < 31 31 but < 38 38 but < 45 45 but < 52 52 but < 59

1 4 10 13 16 19 20

5% 20% 50% 65% 80% 95% 100%

5 26

2

Describing Data: Graphical

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% 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 Construct a pie chart to show this informati information. on. ANSWER: Level of Employment Pie Chart

Executive

Technical

10% 10%

20% 20%

Executive

Professional

Professional

15% 15%

Clerical Administrative Administrative

Technical

Clerical

30% 30%

25% 25%

71.

Construct Construct a bar chart to show this informati information. on. ANSWER:

Level of Employment Bar Chart 35 30 y c 25 n e 20 u q 15 e r 10 F 5 0

30 25 20 15 10

E  x  e c  u t    i     v  e

P  r   o f    e s  s  i     o n a l    

C  l     e r   i     c  a l    

A  d   m i     n i     s  t    r   a t    i     v  e

T  e c  h   n i     c  a l    

27

Chapter 2

72.

Brief Briefly ly discus discuss s the Pareto Pareto diagr diagram. am. ANSWER:

A Pareto diagram, named after the Italian economist Vilfredo Pareto, is a bar chart that displays the frequency of defect defect causes. The bar at the left indicates indicates the most frequent cause and bars to the right indicate indicate causes with with decreasing decreasing frequencies. frequencies. A Pareto diagram is used to separate the “vital few” from the “trivial many”. 73.

A company company has determine determined d that that there there are are seven seven possible possible defects defects for for one one of its product product lines. Construct a Pareto diagram for the the following defect frequencies: frequencies: Defe Defect ct Code Code

Freq Freque uenc ncy  y 

A B C D E F G

10 70 15 90 8 4 3

ANSWER:

Pareto Chart of Defects 200 200

100

80 150 150

t n u o C

60 100 100 40

50 20

0 Defective Code Count

0 D 90

B 70

C 15

A 10

E 8

Other 7

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.

28

Year 1999 2000 2001 2002 2003 2004 2005

Bachelor 510 498 481 472 441 441 497

Graduate 85 85 94 110 93 119 169

Law 223 263 270 270 252 282 217

Describing Data: Graphical

74.

Graph Graph the data data with with a time-s time-seri eries es plot. plot. ANSWER:

T ime series series plot plot of degrees aw arded from 1999 to 2 525

450

375

s e e r 300 g e d f o r e b 225 m u N

Bac Gra La

150

75

75.

What possible possible conclusion conclusions s or actions actions might the universit university y consider? consider? ANSWER:

Year 

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

29

Chapter 2 33.2 31.1

28.3 32.6

20.6 49.9

39.8 31.1

30.6 38.3

19.0

20.6

76

Constr Construct uct a histog histogram ram to descri describe be the data. data.

37.1

24.8

29.9

40

45

ANSWER:

Histogra 10 8 y c 6 n e u q 4 re F

2 0 15

77.

30

20

25

Constr Construct uct an ogive ogive to descri describe be the data. data.

30

35

50

Describing Data: Graphical ANSWER:

100% 78.

Draw a stem-and-l stem-and-leaf eaf display display to describe describe the data. ANSWER:

StemQUESTIONS 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 5.2 79.

5.8 6.7

4.5 3.0

6.2 2.4

4.8 5.0

7.3 3.6

4.6 2.9

3.9 4.0

4.4 2.8

5.5 3.6

Stem uni unit: 10 Steme

Construct Construct a stem-and-l stem-and-leaf eaf display display for the data

ANSWER:

g

31

Chapter 2

80.

Describe Describe graphicall graphically y the the time (in hours) hours) that students students studied studied for the test ANSWER:

Histogram 7 6 c n e u q e r F

5 4 3 2 1 0 3

4.5

6

7.5

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 Freshman Sophomore Junior Senior Total 81.

A ∗

14 17 5 ∗

B 17 23 19 8 67

C 28 17 10 4 59

D 8 10 2 0 20

F 3 1 1

To Total 69 ∗

∗

49 17

5

∗

Calcul Calculate ate the the missi missing ng values values iden identif tified ied by by asteri asterisks sks.. What patt pattern erns s do you you see in this this table? ANSWER:

Year Freshman Sophomore Junior Senior Total

A 13 14 17 5 49

B 17 23 19 8 67

C 28 17 10 4 59

D 8 10 2 0 20

F 3 1 1 0 5

Total 69 65 49 17 200

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

32

Describing Data: Graphical 82.

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

Year Freshman Sophomore Junior Senior Total

A 6.5% 7.0% 8.5% 2.5% 24.5%

B 8.5% 11.5% 9.5% 4.0% 33 3 3.5%

C 14.0% 8.5% 5.0% 2.0% 29 2 9.5%

D 4.0% 5.0% 1.0% 0.0% 10%

F 1.5% 0.5% 0.5% 0.0% 2.5%

Total 34.5% 32.5% 24.5% 8.5% 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 comple completing ting a survey, survey, respondent respondents s use use the the follow following ing numbers numbers to to indica indicate te marita maritall status. 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. meaningless.

84.

A consum consumer er goods goods company company has has been been studyi studying ng the the effect effect of adverti advertising sing on total total profits. profits. As part of this study, data on advertising expenditures ($1000s) and total sales ($1000s) were collected collected for a five-month period and are are as follows: follows: (15, 150), (22.5, 300), (10.5, 120), (18, 180), and (21, 225), where the first number is 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:

Scatter Plot 350

300

250 e l a 200 S l a t 150 o T

100

50

0 5

10

15

Advertising Expenditures

20

33

Chapter 2

Clearly the is a positive relationship between advertising expenditures and total sales. 85.

In completing completing a survey, survey, respondent respondents s use use the following following numbers numbers to indicate 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 Explain the differenc difference e between between the terms terms “varia “variable” ble” and “data.” “data.” Include Include an illustrat illustration ion that demonstrates this difference. ANSWER:

Variable: Variable: a characteri characteristic stic of interest interest about each individual individual element of a populatio population n 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).

87.

A departmen departmentt of mathematic mathematical al sciences sciences has majors majors in four areas. areas. Major

Number of Majors

Mathematics Computer Science Actuarial Science Statistics

50 22 15 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 Computer Science Actuarial Science Statistics

51.5 22.7 15.5 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  Count 

34

Blemish 61

Scratch 50

Chip 28

Bend 17

Dent 13

Others 11

Describing Data: Graphical

Pareto Chart for Product Defects 180

1 0.8

120

0.6

t n u o C

0.4

60

t n e c r e P

0.2 0

0 Blem

Scratch

Chip

Bend

Dent

Others

Defect type

88.

What What is the total total defect defect count count in the report report? ? ANSWER:

180 defects 89.

Find the percentage for “chip” defect items. ANSWER:

Percent of chip = (50/180) ⋅ 100% = 15.56% 90.

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

Managem Management ent has has given given the the produc productio tion n line line the goal goal of of reduci reducing ng their their defe defects cts by by 50%. 50%. What two defects would you suggest they give special attention to in working toward this goal? Explain. ANSWER:

The two defects, defects, Blemish Blemish and Scratch, Scratch, total 61.67%. 61.67%. defects, the goal should be within reach.

If they can control these these two

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 Pareto diagram diagram picturing picturing the “Presents “Presents not wanted”. wanted”. ANSWER:

35

Chapter 2

Pareto Pareto Diagram for Unwanted Presents 100

t n u o C

100

80

80

60

60

40

40

20

20

0

0

Unwanted Presens Presens Count

93.

Teddy Bears 45

Chocolate 25

J ewelry elry 15

Flowers 12

Other 3

If you you want want to to be 80% 80% sure sure you did did not not get your your valent valentine ine some somethi thing ng unwan unwanted ted,, what 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 adul adults ts are are to be surv surveye eyed, d, what what freq frequen uencie cies s would would you you expect expect to to occur occur for for each each unwanted item listed on the snapshot? ANSWER:

95. 95.

The frequencies are 180, 100, 60, 48, and 12 for teddy bears, chocolates, jewelry, flowers, and don’t know, respectively. The The student students s at small small commun communit ity y colle college ge in Iowa Iowa apply apply to study study eithe eitherr Englis English h or  Business. Business. Some administr administrators ators at the college college are concerned that women women are being discriminated against in being allowed admittance, particularly in the business program. Below, Below, you will will find find two two contin contingenc gency y tables tables that that show show the percen percentag tage e of studen students ts admitted by gender to the English English program and the Business school. The data has also been presented graphically. What do the data and graphs indicate? English program

Gender Female Male Total

No 46.0% 60.8% 53.5%

Yes 54.0% 39.2% 46.5%

Business school 

Total 100% 100% 100%

Gender Female Male Total

No 69.2% 64.1% 65.4%

Yes 30.8% 35.9% 34.6%

Total 100% 100% 100%

Percent of Business Student Admitted

Percent Admitted by Gend Female

80.0%

Female

60.0%

60.0%

Male

40.0%

40.0%

Male

80.0%

20.0%

20.0%

0.0% No

36

Ye s

M    a   F    e   e  m   l    a  l    e  

0.0% No

Yes

M    a  l    e   F    e  m   a  l    e  

Describing Data: Graphical 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 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 the final. The following table contains contains the result.

Studying for Exam Went Partying 96.

Did Did Well Well in Exam Exam 60 22

Did Did Poor Poorly ly in Exam Exam 15 53

Of those those in in the samp sample le who who went went party partying ing the the weeke weekend nd before before the the final final exam exam,, what what percentage of them did well in the exam? ANSWER:

22 out of 75, or 29.33% 97.

Of thos those e in the the sampl sample e who did did well well on on the final final exam, exam, what what percen percentag tage e of them them went went partying the weekend before the exam? ANSWER:

22 out of 82, or 26.83%

98.

What What percen percentag tage e of the the studen students ts in the the sampl sample e went went partyi partying ng the the weeken weekend d before before the the final exam and did well in the exam? ANSWER:

22 out of 150, or 14.67% 99.

What percentage percentage of the students students in the sample sample spent spent the weekend weekend studyin studying g and and did did well well in the final exam? ANSWER:

60 out of 150, or 40% 100. 100.

What What percent percentage age of the stude students nts in the sampl sample e went partyi partying ng the weeken weekend d before before the final exam and did poorly on the exam? ANSWER:

53 out of 150, or 35.33% 101.

If the the sample sample is a good represe representati ntation on of the the populati population, on, what what percent percentage age of the students 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%

37

Chapter 2 102.

If the the sample sample is a good good represen representati tation on of the the populati population, on, what what percenta percentage ge of those those who who spent the weekend studying should we expect to do poorly o n the final exam? ANSWER:

15 out of 75, or 20% 103.

If the the sample sample is a good good represen representati tation on of the the populati population, on, what what percenta percentage ge of those those who 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. 104.

Of those those in the sample sample who who went partyi partying ng the weeken weekend d before before the final final exam, exam, what percentage of them did poorly in the exam? ANSWER:

53 out of 75, or 70.67% 105.

Of those those in the sample sample who who did well in the the final final exam, exam, what what percentag percentage e of them them spent spent the the weekend before the exam studying? ANSWER:

60 out of 82, or 73.17%

106.

The data data in the the time time series series plot below represents represents monthly monthly sales sales for two years years of beanba beanbag g 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. Time Time series chart of S

52 5 45 0 37 5 s e l 30 0 a S

22 5 15 0 75 1

2

3

4

5

6

7

8

9

1 0 1 1 1 2 13 13 1 4 1 5 1 6 1 7 1 8 1 9 2 0 2 1 2 2 2 3 2 4 Observation Num

ANSWER:

38

Describing Data: Graphical This is a representation representation of seasonal data. There seems to be a small small increase in months 3, 4, and 5 and a large increase increase at the end of the year. year. The sales of this this item seem to peak in December and have a significant drop off in January. 107. 107.

The 2005 2005 mobile mobile phone manufa manufactu cturer rers' s' global global market market shares shares were as follows follows:: Nokia Nokia 26.9%, 26.9%, Motoro Motorola la 16.9%, 16.9%, Ericso Ericson n 10.5%, 10.5%, Samsun Samsung g 6.2%, 6.2%, Panaso Panasonic nic 5.5%, 5.5%, others others (Siemens, Alcatel, Mitsubishi, Philips, NEC, and more) 34.0%. Present this information in a pie chart. ANSWER:

Nokia 27%

Others 33%

Panasonic 6% Samsung 6%

108. 108.

Motorola 17% Ericson 11%

Creat eate a time-series line graph showing U.S. federal government deficits (-) or surpluses (+) for 1975-1999 (in billions of dollars): -69.3 -53.7 -147.9 -274.2 +124.4

-53.0 -132.6 -137.3 -212.3

-45.1 -173.9 -130.0 -192.0

-26.9 -168.0 -173.0 -136.8

-11.3 -177.2 -215.3 -53.3

-53.8 -192.1 -297.6 +49.0

ANSWER:

39

Chapter 2

150 100 50 0 -50 -100 -150 -200 -250 -300 -350 1975

40

1980

1985

1990

1995 1995

2000 2000