CHAPTER 2 GRAPHICAL DESCRIPTIVE TECHNIQUES MULTIPLE...

CHAPTER 2 GRAPHICAL DESCRIPTIVE TECHNIQ UES

MULTIPLE CHOICE QUESTIONS

1. The most appropriate type of chart for determining the numb er of observa tions at or below a specific value is:a. a histogra mb. a pie chartc. a time series chartd. a cumulative frequency ogiveANSWER: d

2. The best type of chart for comparing two sets of categorical data is:a. a line chartb. a pie chartc. a histogra md. a bar chartANSWER: d

3. The total area of the six bars in a relative frequency histogra m for which the width of each bar is five units is:a. 6b. 5c. 11d. 1ANSWER: b

4. Which of the following state m e n t s about pie charts is false?a. Pie charts are graphical represe n t a t ions of the relative frequency

distributionb. Pie charts are usually used to display the relative sizes of categories for

interval data. c. Pie charts always have the shape of a circled. Area of each slice of a pie chart is the proportion of the corresponding

category of the frequency distribution of a categorical variableANSWER: b

5. The total area of the bars in a relative frequency histogra m:a. depend s on the sample sizeb. depend s on the numb er of barsc. depend s on the width of each bard. Both a and bANSWER: c

6. Which of the following state m e n t s is false?a. All calculations are permit ted on interval datab. All calculations are permit ted on nominal datac. The most important aspec t of ordinal data is the order of the data values

6

7 Chapter Two

d. The only permissible calculations on ordinal data are ones involving a ranking process

ANSWER: b

7. Which of the following state m e n t s is false?a. A frequency distribution counts the numb er of observa tions that fall into

each of a series on intervals, called classes that cover the complet e range of observa tions .

b. The intervals in a frequency distribution may overlap to ensure that each observa tion is assigned to an interval

c. Although the frequency distribution provides information about how the numb ers in the data set are distributed, the information is more easily unders tood and impart ed by drawing a histogra m

d. The number of class intervals we select in a frequency distribution depend s entirely on the numb er of observa tions in the data set

ANSWER: b

8. In general , incomes of employee s in large firms tend to bea. positively skewedb. negatively skewedc. symm e t ricd. None of the aboveANSWER: a

9. The relative frequency of a class is comput ed bya. dividing the frequency of the class by the numb er of classesb. dividing the frequency of the class by the class widthc. dividing the frequency of the class by the total number of observa tions in

the data setd. subtracting the lower limit of the class from the upper limit and

multiplying the difference by the numb er of classesANSWER: c

10. A modal class is the class that includes a. the largest number of observa tionsb. the smalles t numb er of observa tionsc. the largest observa tion in the data setd. the smalles t observa tion in the data setANSWER: a

11. The sum of the relative frequencies for all classes will always equala. the numb er of classesb. the class widthc. the total numb er of observa tions in the data setd. oneANSWER: d

12. The two graphical techniques we usually use to present nominal data area. bar chart and histogra m b. pie chart and ogive

Graphical

Descriptive Technique s 8

c. bar chart and pie chart d. histogra m and ogiveANSWER: c

13. The most important and commonly graphical presen t a t ion of interval data is aa. bar chartb. histogra mc. pie chartd. cumula tive frequency distributionANSWER: b

14. The relationship betwee n two interval variables is graphically displayed by aa. scatt er diagra mb. histogra mc. bar chartd. pie chartANSWER: a

TRUE/FALSE QUESTIO NS

15. A relative frequency distribution describes the proportion of data values that fall within each class, and may be present e d in a histogra m form.ANSWER: T

16. A cumulative frequency distribution lists the numb er of observa tions that are within or below each of the classes . ANSWER: T

17. The stem and leaf display reveals far more information relative to individual

values than does the histogra m.ANSWER: F

18. Individual observa tions within each class may be found in a frequency distribution.ANSWER: F

19. Compared to the frequency distribution, the stem and leaf display provides more details, since it can describe the individual data values as well as show how many are in each group, or stem.ANSWER: T

20. A relative frequency distribution describes the proportion of data values that fall within each category.ANSWER: T

21. The following stem and leaf output has been genera t e d by Minitab. This data has a nega tive mode.

9 Chapter Two

Stem and leaf of C2 N = 75Leaf Unit = 0.01

1 2 62 2 05 1 5558 1 42022 0 999998877 7 7 6 6 536 0 443221111 1 1 0 0 0(14) 0 01122233 3 3 3 3 4 425 0 66678889 9 9 914 1 00222223 3 44 1 562 2 03

ANSWER: T

22. The following stem and leaf output has been genera t e d by Minitab. The median of this data is 26.

Stem and leaf of C2 N = 75Leaf Unit = 10

9 0 00011233 314 0 5689921 1 000012326 1 6669933 2 3334445(8) 2 6667788834 3 002334427 3 5666999919 4 00012223 310 4 55566677 9 9

ANSWER: F

23. The class interval in a frequency distribution is the numb er of data values falling within each class.ANSWER: F

24. In the term “frequency distribution,” frequency refers to the numb er of data values falling within each class.ANSWER: T

Graphical


25. The difference betwee n a histogra m and a bar chart is that the histogra m represe n t s nominal data while the bar chart represe n t s interval data .ANSWER: F

26. The largest value in a set of data is 140, and the lowest value is 70. If the resulting frequency distribution is to have five classes of equal width, the class width will be 14.ANSWER: T

27. A stem and leaf display describes two digit integers betwee n 20 and 70. For one of the classes displayed, the row appe ar s as 4|256. The numerical values being described are 24, 54, and 64.ANSWER: F

28. The total area of the six bars in a relative frequency histogra m for which the width of each bar is five units is 1.ANSWER: F

29 The following “charact e r histogra m” has been genera t e d by Minitab. The median class is 150.

Histogra m of C1 N = 75

Midpoint Count150 1 *100 1 *50 3 *** 0 2 **50 7 *******100 12 ************150 18 ******************200 20 ********************250 5 *****300 5 *****350 1 *

ANSWER: T

30. The following stem and leaf output has been genera t e d by Minitab. This data set has a mean that is nega tive, and there is no modal class.

Stem and leaf of C2 N = 10Leaf Unit = 0.10

2 1 534 0 97(2) 0 654 0 33 0 62 1 3

11 Chapter Two

1 1 8

ANSWER: T

31. A frequency distribution is a listing of the individual observa tions arrang ed in ascending or descending order.ANSWER: F

32. A cumulative frequency distribution when present e d in graphic form is called an ogive.ANSWER: T

33. Nominal data are also called qualitative or categorical data.ANSWER: T

34. A variable is some charact e ris tic of a population, while data are the observed values of a variable based on a sample.ANSWER: F

35. Interval data, such as heights, weights, and incomes , are also referred to as quanti ta tive or numerical data .

ANSWER: T

36. There are actually four types of data: nominal, ordinal, interval, and ratio. However, for statistical purposes , there is no difference betwe en interval and ratio data , and the authors of your book combine the two types .ANSWER: T

37. Ordinal data may be treat e d as interval but not as nominal.ANSWER: F

38. Interval data may be treat ed as ordinal or nominal.ANSWER: T

39. Nominal data may be treat e d as ordinal or intervalANSWER: F

40. A histogra m is said to be symm et ric if, when we draw a vertical line down the center of the histogra m, the two sides are identical in shape and size.ANSWER: T

41. A skewed histogra m is one with a long tail extending either to the right or left. The former is called nega tively skewed, and the later is called positively skewed.ANSWER: F

42. A bimodal histogra m is one with two peaks equal in height .ANSWER: F

Graphical


43. Bar and pie charts are graphical techniques for nominal data . The former focus the atten tion on the frequency of the occurrence s of the categories , and the later emph asize the proportion of occurrence s of each category.ANSWER: T

44. The graphical technique used to describe the relationship betwe e n two interval variables is the scatt er diagra m.ANSWER: T

45. If we draw a straight line through the points in a scatt er diagra m and most of the points fall close to the line, we say that there is a positive linear relationship betwee n the two variables .ANSWER: F

46. Time series data are often graphically depicted on a line chart , which is a plot of the variable of interes t over time.ANSWER: T

47. Professor Hogg gradua t e d from the University of Iowa with a code value = 2 while professor Maas gradua t e d from Michigan State University with a code value = 1. The scale of measure m e n t likely represe n t e d by this information is ratio. ANSWER: F

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

49. Quantita tive variables usually represe n t memb ers hip in groups or categories . ANSWER: F

50. An automobile insurance agent believes that compa ny “A” is more reliable than company “B”. The scale of measure m e n t that this information represe n t s is the ordinal scale. ANSWER: T

51. When a distribution has more values to the left and tails to the right, it is skewed negatively.ANSWER: F

52. When a distribution has more values to the right and tails to the left, we say it is skewed positively.ANSWER: F

13 Chapter Two

TEST QUESTIONS

53. Identify the type of data for which each of the following graphs is appropriate .a. Histogra mb. Pie chartc. Bar chart

ANSWERS:a. Intervalb. Nominal c. Nominal

54. Before leaving a particular restaura n t , custom er s are asked to respond to the ques tions listed below. For each ques tion, determine whether the possible respons e s are interval, nominal, or ordinal.a. What is the approxima t e distance of the restaura n t from your residence?b. Have you eaten at the restauran t previously?c. If your answer to part (b) was yes, on how many occasions? d. Which of the following attribute s of the restauran t do you find most

attractive: service, prices, quality of the food, or varied menu?e. Would your overall rating of the restaura n t be excellent , good, fair, or

poor?

ANSWERS:a. Intervalb. Nominalc. Intervald. Nominale. Ordinal

55. For each of the following examples , identify the data type as nominal, ordinal, or interval.a. the letter grades received by student s in a computer science classb. the numb er of studen t s in a statistics coursec. the starting salaries of newly Ph.D. gradua t e s from a statistics progra md. the size of fries (small, medium, large) ordered by a sample of Burger

King custom ers .e. the college (Arts and science, Business , etc.) you are enrolled in.

ANSWERS:a. Ordinal b. Interval c. Interval d. Ordinal e. Nominal

Graphical


56. At the end of an escorted motor coach vacation, the tour opera tor asks the vacationer s to respond to the questions listed below. For each question, deter mine whether the possible respons e s are interval, nominal, or ordinal.a. How many escorted vacations have you taken prior to this one?b. Do you feel that the stay in New York was sufficiently long?c. Which of the following features of the hotel in New York did you find most

attractive: location, facilities, room size, or price?d. What is the maximu m number of hours per day that you would like to

spend traveling?e. Would your overall rating of this tour be excellent , good, fair, or poor?

ANSWERS:a. Intervalb. Nominalc. Nominald. Intervale. Ordinal

57. Provide one example for nominal, ordinal, and interval data.

ANSWER:Nominal data : Political party affiliation for voters recorded using the following code:

Democra t 1, Republican 2, Independ e n t 3. Ordinal data : Respons e to marke t research survey measure d on the Likert scale using the following code: Strongly agree 1, Agree 2, Neutral 3, Disagree 4, and Strongly disagre e 5.Interval data : Tempera tur e in computer labs.

58. For each of the following, indicate whether the variable of interes t would be nominal or interval.a. whether you are a US citizenb. your marital statusc. numb er of cars in a parking lotd. amount of time you spend per week on your homework e. Lily’s travel time from her dorm to the studen t union at the university of

Iowaf. Heidi’s favorite brand of tennis balls.

ANSWERS:a. Nominalb. Nominalc. Intervald. Intervale. Intervalf. Nominal

15 Chapter Two

59. Voters participating in a recent election exit poll in Minnesota were asked to state their political party affiliation. Coding the data 1 for Republican, 2 for Democra t , and 3 for Independ e n t , the data collected were as follows:

3 1 2 3 1 3 3 2 13 3 2 1 1 3 2 3 13 2 3 2 1 1 3

a. Develop a frequency distribution and a proportion distribution for the data. What does the data sugges t about the strength of the political parties in Minnesota?

b. Construct a frequency bar graph.

ANSWERS:a.

Party Frequency Proportion

Republican 8 0.32

Democra t 6 0.24

Independ e n t 11 0.44

Independ e n t in Minnesota is stronger than Republican and Democra t parties

b.

QUESTIONS 60 AND 61 ARE BASED ON THE FOLLOWING INFORMATION:

The ages of a sample of 25 salesper sons are as follows:

47 21 37 53 28 40 30 32 34 2634 24 24 35 45 38 35 28 43 4530 45 31 41 56

60. Manually draw each of the following graphs. a. a histogra m with four classes and a histogra m with six classesb. a stem and leaf displayc. a dot plot

0

2

4

6

8

10

12

Republican Democrat Independent

Fre

qu

en

cy

Graphical


61. Construct an ogive for the data , and estima t e the proportion of salespersons who are:a. less than 30 years of ageb. more than 40 years of agec. betwe en 40 and 50 years of age

ANSWERS:

a. 0.24b. 1 0.64 = 0.36c. 0.92 0.64 = 0.28

62. What is the total area under a relative frequency histogra m for which the width of each class is three units?

ANSWER: 3

63. The numb er of defective items produced by a machine and recorded for the last 25 days are as follows:

19 6 15 20 17 16 17 12 15 29 23 17 7 10 14 14 27 22

8 5 23 19 9 28 5

a. Construct a frequency distribution and relative frequency distribution for these data. Use five class intervals, with the lower boundary of the first class being five items.

b. Construct a relative frequency histogra m for these data.c. What is the relationship betwe e n the total area under the histogra m you

have construc t ed and the relative frequencies of observa tions?

0.00

0.24

0.64

0.921.00

0.0

0.1

0.20.3

0.4

0.5

0.6

0.70.8

0.9

1.0

20 30 40 50 60

Ages (years)

Cu

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17 Chapter Two

ANSWERS:a.

Class Limits Frequency Relative Frequency 5 up to 10* 6 0.2410 up to 15 4 0.1615 up to 20 8 0.3220 up to 25 4 0.1625 up to 30 3 0.12 Total 25 1.00

*Class contains observa tions up to but not including 10. The other classes are defined similarly. This notion is used throughout the chapter .

b.

Note that the numb er s that appear along the horizontal axis represe n t the upper Limits of the class intervals even though they appear in the center of

the classes c. Note that the area under the histogra m betwee n two values is five times the relative frequency of observa tions that fall betwe en those two values (since 5 is the width of

each class). Hence, the total area under the histogra m is therefore equal to 5.

64. The annual gross revenu e s for a growing business are provided below for the last 40 years.

1.02 2.82 4.23 3.24 2.56 6.12 9.88 8.97 9.20 17.2523.28 18.69 18.60 35.12 44.98

0

0.1

0.2

0.3

0.4

10 15 20 25 30

Defective Items

Rel

ativ

e Fr

eque

ncy

Graphical


31.90 24.32 35.28 40.22 27.4121.46 31.05 32.46 19.44 12.7826.50 38.10 31.40 29.64 51.74

65.62 49.84 47.22 85.30 104.9671.77 52.94 74.48 82.56 54.82

a. Plot the time seriesb. Which time period has the largest value?

ANSWERS:a.

b. Time period 35

QUESTIONS 65 THROUGH 72 ARE BASED ON THE FOLLOWING INFORMATION:

The grades on a calculus exam for a sample of 40 studen t s are as follows:

63 74 42 65 51 54 36 56 68 57 62 64 76 67 79 61 81 77 59 3884 68 71 94 71 86 69 75 91 55 48 82 83 54 79 62 68 58 41 47

65. Construct a stem and leaf display for these data .

ANSWER:

Stem Leaf

3 684 12785 1445678 96 1223457 88 8 97 1145679 98 12346

0

20

40

60

80

100

120

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39

Time

Ann

ual G

ross

19 Chapter Two

9 14

66. Construct a frequency distribution and relative frequency distribution for these data, using seven class intervals.

ANSWER:

Class Limits

Frequency Relative Frequency

30 up to 40 2 0.05040 up to 50 4 0.10050 up to 60 8 0.20060 up to 70 11 0.27570 up to 80 8 0.20080 up to 90 5 0.12590 up to 100

2 0.050

Total 40 1.00

67. Construct a relative frequency histogra m for these data.

ANSWER:

68. Describe briefly what the histogra m and the stem and leaf display tell you about the data.

ANSWER:The distribution of the data is symm et rical and bell shaped, with 67.5% of the observa tions betwe en 50 and 80.

0

0.05

0.1

0.15

0.2

0.25

0.3

40 50 60 70 80 90 100

Grade

Rel

ativ

e Fr

eque

ncy

Graphical


69. Construct a cumulative frequency and a cumula tive relative frequency distribution

ANSWER:

Classes Cumulative Frequency

Cumulative Relative Frequency

up to 40 2 0.050up to 50 6 0.150up to 60 14 0.350up to 70 25 0.625up to 80 33 0.825up to 90 38 0.950up to 100 40 1.00

70. What proportion of the grades is less than 60?

ANSWER:0.35

71. What proportion of the grades is more than 70?

ANSWER:1 0.625 = 0.375

72. Construct an ogive, and estima t e the proportion of grades that are betwee n 80 and 90.

ANSWER:

0.0000.050

0.150

0.350

0.625

0.825

0.9501.000

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

30 40 50 60 70 80 90 100

Grade

Cu

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21 Chapter Two

The proportion of grades that are betwee n 80 and 90 = 0.95 0.825 = 0.125.


Car buyers were asked to indicate the car dealer they believed offered the best overall service. The four choices were Carriage Motors (C), Marco Chrysler (M), Triangle Auto (T), and University Chevrolet (U). The following data were obtained.

T C C C U C M T C U U M C M T C M M C MT C C T U M M C C T T U C U T M M C U T

73. Construct a frequency distribution and proportion distribution.

ANSWER:

Dealer Frequency ProportionC 14 0.350M 10 0.250T 9 0.225U 7 0.175

74. Construct a frequency bar chart.

ANSWER:

75. Construct a pie chart.

ANSWER:

0

5

10

15

C M T U

Dealership

Fre

qu

en

cy

C35.0%

M25.0%

T22.5%

U17.5%

Graphical


76. Given the following five categories and the number of times each occurs, manu ally draw a pie chart and a bar chart hand.

Category 1 2 3 4 5Frequency 17 29 40 24 20

77. A professor of econo mics wants to study the relationship betwee n income and educa tion. A sample of 10 individuals is select ed at random, and their income (in thousand of dollars) and educa tion (in years) are shown below:

Education 12 14 10 11 13 8 10 15 13 12Income 25 31 20 24 28 15 21 35 29 27

a. Draw a scatt er diagra m for these data with the income on the vertical axis.

b. Describe the relationship betwe en income and educa tion.

ANSWERS:

a.

b. There is a very strong positive relationship betwe en educa tion and income; as years of educa tion increase , there is a definite tendency for income to linearly increas e .

78. A grocery store’s monthly sales (in thousand s of dollars) for the last year were as follows:

Month 1 2 3 4 5 6 7 8 9 10 11 12Sales 78 74 83 87 85 93 100 105 103 89 78 94

0

5

10

15

20

25

30

35

40

0 5 10 15 20

Education

Inco

me

23 Chapter Two

a. Construct a relative frequency bar chart for these data .b. Construct a line chart.

ANSWERS:a.

b.

79. Consider the following cumulative frequency distribution.

Classes Limits

Cumulative Frequency

Up to 5 8Up to 10 15

0.00

0.02

0.04

0.06

0.08

0.10

0.12Ja

n.

Feb.

Mar

ch

Apr

il

May

June

July

Aug

.

Sep

t.

Oct

.

Nov

.

Dec

.

Month

Rel

ativ

e F

requ

ency

0

30

60

90

120

Jan.

Feb.

Mar

ch

Apr

il

May

Jun

e

July

Aug

.

Sep

t.

Oct

.

Nov

.

Dec

.

Month

Sal

es

Graphical


Up to 15 21Up to 20 30Up to 25 42

Find the frequency for each of the following classes . a. 0 up to 5b. 5 up to 10c. 10 up to 15d. 15 up to 20e. 20 up to 25

ANSWERS:a. 8b. 7c. 6d. 9e. 12


The frequency distribution for a sample of 200 business school gradua t e s is shown in the following table.

Major of Gradua t e s

Number of gradua t e s

Accounting 58Finance 42Manage m e n t 38Marketing 52Other 10

80. Construct a relative frequency distribution.

ANSWER:

Major of Graduat e s

Proportion of Graduat e s

Accounting 0.29Finance 0.21Manage m e n t 0.19Marketing 0.26Other 0.05Total 1.00

25 Chapter Two

81. Draw a pie chart of the numb er of gradua t e s .

ANSWER:

82. Draw a frequency bar chart .

ANSWER:

83. The weights in pounds of a sample of 25 workers are given below:

164 148 137 157 173 156 177 172 169 165145 168 163 162 174 152 156 168 154 151174 146 134 140 171

010203040506070

Acc

ount

ing

Fina

nce

Man

agem

ent

Mar

ketin

g

Oth

er

Major

Fre

qu

en

cy

Accounting29.0%

Finance21.0%

Management19.0%

Marketing26.0%

Other5.0%

Graphical


a. Construct an ogive for the data.b. What proportion of the total area under the ogive construct e d in part (a)

falls betwee n 160 and 180?

ANSWERS:

a.

b. 1 0.48 = 0.52

84. The number of houses sold in Grand Rapids and the averag e monthly mortgag e rates for 18 months randomly select ed betwee n January 1997 and April 1999 are shown in the following table.

Mortgag e rate (%)

Number of houses sold

Mortgag e rate (%)

Number of houses sold

7.5 90 9.5 689.0 72 6.5 977.0 89 8.0 79

10.5 62 9.0 7510.0 58 10.5 539.5 70 9.5 738.5 74 11.0 50

10.0 65 7.5 8211.0 51 8.5 70

a. Draw a scatt er diagra m with the number of houses sold on the vertical axis.

0.000.08

0.24

0.48

0.76

1.00

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

130 140 150 160 170 180

Weight (pounds)

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27 Chapter Two

b. Describe the relationship betwe en mortgag e rate and numb er of houses sold.

ANSWERS:a.

b. There is a strong linear relationship betwe e n the mortgag e rate and the numb er of houses sold.


The frequency distribution of the numb er of years of service for 100 employee s is shown below:

Years Frequency0 up to 5 12

5 up to 10 1610 up to 15 4215 up to 20 2020 up to 25 10

Total 100

85. Construct a relative frequency distribution for the data .

ANSWER:

Years Relative Frequency0 up to 5 0.12

5 up to 10 0.16

0

20

40

60

80

100

120

0 2 4 6 8 10 12

Mortgage Rate (%)

Nu

mb

er

of H

ou

se

s S

old

Graphical


10 up to 15 0.4215 up to 20 0.2020 up to 25 0.10

Total 1.00

86. Construct a cumula tive relative frequency distribution for the data .

ANSWER:

Years Cumulative Relative Frequency

up to 5 0.12up to 10 0.28up to 15 0.70up to 20 0.90up to 25 1.00

87. Estimate the proportion of employees who have:a. less than 10 years of service.b. more than 20 years of service.c. betwe en 10 and 20 years of service.

ANSWERS:a. 0.28b. 1 0.90 = 0.10c. 0.90 0.28 = 0.62

CHAPTER 2 GRAPHICAL DESCRIPTIVE TECHNIQUES MULTIPLE...

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