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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
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.
Bin / Frequency / Cumulative %10 / 1 / 5.00%
15 / 9 / 50.00%
20 / 1 / 55.00%
25 / 7 / 90.00%
More / 2 / 100.00%
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)Sevenworkers 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?
Bin / Frequency / Cumulative %12.8 / 1 / 5.00%
41.6 / 5 / 30.00%
70.4 / 6 / 60.00%
99.2 / 6 / *
More / 2 / 100.00%
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
8.Data on the monthly expenses (in $) submitted by 15 people on a firm’s sales staffare summarized in the following stem-and-leaf display.
Stem-and-leaf
Dollars N = 25
Leaf Unit = 10.0
22 5 7
(7)3 1 1 4 5 6 7 8
54 2 2 4 5 9
15 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
25 0 4 8
56 0 0 2 4 5 9
(11)7 0 0 2 2 3 3 5 5 7 7 8
68 0 0 2 3 7 8
39 2 2 7
110 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 MichiganState 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
11.Consider the following frequency distribution generated by Excel. What proportion of these values are less than 63?
Bin / Frequency / Cumulative %26 / 0 / 0.00%
44.5 / 5 / 25.00%
63 / 7 / 60.00%
81.5 / 1 / 65.00%
More / 7 / 100.00%
A)25%
B)60%
C)65%
D)35%
ANSWER:A
12.Companies are often interested in knowing how customers learned about their products. They often solicit this information on mail-in warranty cards. The customers’ responses for a particular product were gathered and the data are presented in the pie chart below.
What percentage of respondents learned about the product through television or the Internet?
A)12%
B)39%
C)51%
D)100%
ANSWER:C
13.Pareto’s result is applied to a wide variety of behavior over many systems. It is sometimes referred to as the
A)“20-80” Rule
B)“80-20” Rule
C)“10-90” Rule
D)“90-10” Rule
ANSWER:B
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:
SingleMale / 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
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
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 / TotalBrand 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
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
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
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
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
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:
QUESTIONS 59THROUGH63 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.
2.84.90.513.214.28.93.715.211.213.4
5.510.21.114.27.84.510.98.818.217.1
59.Construct a stem-and-leaf display of the data.
ANSWER:
60.Construct a frequency distribution of the data.
ANSWER:
Time(in hours) / Frequency0 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
61.Construct cumulative frequency and cumulative percentage distributionsof 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%
62.Use your answer to Question 60to 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 64AND 65ARE 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:
Bins / Frequency2.0 / 1
4.5 / 4
7.0 / 0
9.5 / 1
12.0 / 4
65.Use your answer to Question 64to construct a histogram of the data
ANSWER:
66.The sales manager for a local commercial waste disposal company has tracked the yearly dollar value (in $1000) of contracts made by both internal sales people and external sales people. The data are presented below. Graph the data with a time plot. What possible conclusions or actions might the firm consider?
Year / 1996 / 1997 / 1998 / 1999 / 2000 / 2001Internal Sales / $357 / 375 / 412 / 368 / 345 / 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.
QUESTIONS 67THROUGH69ARE BASED ON THE FOLLOWING INFORMATION:
Data were collected on the number of people entering an electronics store each hour. The data are presented below.
23354228291738214952
46372549372528132943
67.Construct a stem-and-leaf display of the data.
ANSWER:
68.Construct a frequency distribution of the data.
ANSWER:
Number of People / Frequency10 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
69.Construct cumulative frequency and cumulative percentage distributions of the data.
ANSWER:
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%
QUESTIONS 70AND 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”.
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:
Defect Code / FrequencyA / 10
B / 70
C / 15
D / 90
E / 8
F / 4
G / 3
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.
Year / Bachelor / Graduate / Law1999 / 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
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 dayare displayed below.
24.313.619.725.031.021.824.931.520.225.9
33.228.320.639.830.619.020.637.124.829.9
31.132.649.931.138.3
76Construct a histogram to describe the data.
ANSWER:
77.Construct an ogive to describe the data.
ANSWER:
78.Draw a stem-and-leaf display to describe the data.
ANSWER:
QUESTIONS 79AND 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:
QUESTIONS 81 AND 82 ARE BASED ON THE FOLLOWING INFORMATION:
A statistics professor has developed the cross table presented below, that compares students’ class standing with their final grades.
Year / A / B / C / D / F / TotalFreshman / / 17 / 28 / 8 / 3 / 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:
Year / A / B / C / D / F / TotalFreshman / 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:
Year / A / B / C / D / F / TotalFreshman / 6.5% / 8.5% / 14.0% / 4.0% / 1.5% / 34.5%
Sophomore / 7.0% / 11.5% / 8.5% / 5.0% / 0.5% / 32.5%
Junior / 8.5% / 9.5% / 5.0% / 1.0% / 0.5% / 24.5%
Senior / 2.5% / 4.0% / 2.0% / 0.0% / 0.0% / 8.5%
Total / 24.5% / 33.5% / 29.5% / 10% / 2.5% / 100%
The percentages of students failing the class for freshmen, sophomores, juniors, and seniors are 1.5%, 0.5%, 0.5% and 0.0%, respectively. It appears that the earlier a student is in his or her college career, the worse they will do in class.
83.In completing a survey, respondents use the following numbers to indicate marital status.
1 = Single (never married),