false

Description

CHAPTER 2
GRAPHICAL AND TABULAR
DESCRIPTIVE TECHNIQUES
SECTIONS 1
MULTIPLE CHOICE QUESTIONS
In the following multiple-choice questions, please circle the correct answer.
1. Which of the following statements is false?
a. Allcalculations are permitted on interval data
b. Allcalculations are permitted on nominal data
c. The most important aspect of ordinal data is the order of the data values
d. The only permissible calculations on ordinal data are ones involving a ranking
process
ANSWER: b
2. The average number of units earned per semester by college students is suspected to be
rising. A researcher at Boston College wishes to estimate the number of units earned by
students during the spring semester of 2004 at Boston. To do so, he randomly selects 250
student transcripts and records the number of units each student earned in the spring term
of 2004. The variable of interest to the researcher is the
a. number of students enrolled at Boston College during the spring term of 2004
b. average indebtedness of Boston College students enrolled in the spring
c. age of Boston College students enrolled in the spring
d. number of units earned by Boston College students during the spring term of
2004
ANSWER: d
13 14 Chapter Two
3. The classification of student major (accounting, economics, management, marketing,
other) is an example of
a. a categorical random variable.
b. a discrete random variable
c. a continuous random variable
d. a parameter.
ANSWER: a
4. A study is under way in national forest to determine the adult height of pine trees.
Specifically, the study is attempting to determine what factors aid a tree in reaching
heights greater than 50 feet tall. It is estimated that the forest contains 32,000 adult pines.
The study involves collecting heights from 500 randomly selected adult pine trees and
analyzing the results. The variable of interest in the study is the
a. age of a pine tree in the national forest.
b. height of a pine tree in the national forest.
c. number of pine trees in the national forest.
d. species of trees in the national forest.
ANSWER: b
5. The classification of student class designation (freshman, sophomore, junior, senior) is an
example of
a. a categorical random variable.
b. a discrete random variable.
c. a continuous random variable.
d. a parameter.
ANSWER: a
6. Most analysts focus on the cost of tuition as the way to measure the cost of a college
education. But incidentals, such as textbook costs, are rarely considered. A researcher at
Ferris State University wishes to estimate the textbook costs of first-year students at
Ferris. To do so, he monitored the textbook cost of 200 first-year students and found that
their average textbook cost was $275 per semester. The variable of interest to the
researcher is the
a. textbook cost of first-year Ferris State University students.
b. year in school of Ferris State University students.
c. age of Ferris State University students.
d. cost of incidental expenses of Ferris State University students.
ANSWER: a Graphical and Tabular Descriptive Techniques
15
7. The manager of the customer service division of a major consumer electronics company is
interested in determining whether the customers who have purchased a videocassette
recorder made by the company over the past 12 months are satisfied with their products.
The possible responses to the question “Are you happy, indifferent, or unhappy with the
performance per dollar spent on the videocassette recorder?” are values from a
a. discrete numerical random variable.
b. continuous numerical random variable
c. categorical random variable.
d. parameter.
ANSWER: c 16 Chapter Two
TRUE / FALSE QUESTIONS
8. There are actually four types of data: nominal, ordinal, interval, and ratio. However, for
statistical purposes, there is no difference between interval and ratio data, and the authors
of your book combine the two types.
ANSWER: T
9. Quantitative variables usuallyrepresent membership in groups or categories.
ANSWER: F
10. Interval data, such as heights, weights, and incomes, are also referred to as quantitative or
numerical data.
ANSWER: T
11. Nominal data are also called qualitative or categorical data.
ANSWER: T
12. ATP singles rankings for tennis players is an example of an interval scale.
ANSWER: F
13. Interval data may be treated as ordinal or nominal.
ANSWER: T
14. Nominal data may be treated as ordinal or interval
ANSWER: F
15. Professor Hogg graduated from the University of Iowa with a code value = 2 while
Professor Maas graduated from Michigan State University with a code value = 1. The
scale of measurement likelyrepresented by this information is interval.
ANSWER: F
16. Ordinal data may be treated as interval but not as nominal.
ANSWER: F
17. A variable is some characteristic of a population, while data are the observed values of a
variable based on a sample.
ANSWER: F
18. An automobile insurance agent believes that company “A” is more reliable than company
“B”. The scale of measurement that this information represents is the ordinal scale.
ANSWER: T Graphical and Tabular Descriptive Techniques
17
STATISTICAL CONCEPTS & APPLIED QUESTIONS
19. The Dean of Students conducted a survey on campus. SAT score in mathematics is an
example of a __________, or __________ variable.
ANSWER:
quantitative, numerical
20. Provide one example for nominal, ordinal, and interval data.
ANSWER:
Nominal data example: Political party affiliation for voters recorded using the code: 1 =
Democrat, 2 = Republican, and 3 = Independent.
Ordinal data example: Response to market research survey measured on the Likert
scale using the code: 1 = Strongly agree, 2 = Agree, 3 = Neutral, 4 = Disagree, and 5 =
Strongly disagree.
Interval data example: Temperature in tennis courts during the US Open
21. The dean of students conducted a survey on campus. The gender of the student is an
example of a __________, or __________ variable.
ANSWER:
categorical, qualitative
22. For each of the following examples, identifythe data type as nominal, ordinal, or interval.
a. The letter grades received by students in a computer science class
b. The number of students in a statistics course
c. The starting salaries of newlyPh.D. graduates from a statistics program
d. The size of fries (small, medium, large) ordered by a sample of Burger King
customers
e. The college you are enrolled in (Arts and science, Business, Education, etc.)
ANSWER:
a. Ordinal
b. Interval
c. Interval
d. Ordinal
e. Nominal
23. The Dean of Students conducted a survey on campus. Class designation (Freshman,
Sophomore, Junior, and Senior) is an example of a __________, or __________ variable.
ANSWER:
categorical, qualitative 18 Chapter Two
24. Most colleges admit students based on their achievements in a number of different areas.
The grade obtained in senior level English course (A, B, C, D, or F) is an example of a
__________, or __________ variable.
ANSWER:
categorical, qualitative
25. At the end of an escorted motor coach vacation, the tour operator asks the vacationers to
respond to the questions listed below. For each question, determine whether the possible
responses 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 sufficientlylong?
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 maximum 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?
ANSWER:
a. Interval
b. Nominal
c. Nominal
d. Interval
e. Ordinal
26. For each of the following, indicate whether the variable of interest would be nominal or
interval.
a. Whether you are a US citizen
b. Your marital status
c. Number of cars in a parking lot
d. Amount of time you spend per week on your homework
e. Lily’s travel time from her dorm to the student union at the university of Iowa
f. Heidi’s favorite brand of tennis balls.
ANSWER:
a. Nominal
b. Nominal
c. Interval
d. Interval
e. Interval
f. Nominal
27. In purchasing a used automobile, there are a number of variables to consider. The age of
the car is an example of a __________, or __________ variable. Graphical and Tabular Descriptive Techniques
19
ANSWER:
quantitative, numerical
28. In purchasing an automobile, there are a number of variables to consider. The body style
of the car (sedan, coupe, wagon, etc.) is an example of a __________, or __________
variable.
ANSWER:
categorical, qualitative
29. Before leaving a particular restaurant, customers are asked to respond to the questions
listed below. For each question, determine whether the possible responses are interval,
nominal, or ordinal.
a. What is the approximate distance of the restaurant from your residence?
b. Have you eaten at the restaurant previously?
c. On how many occasions have you eaten at the restaurant previously?
d. Which of the following attributes of the restaurant do you find most attractive:
service, prices, quality of the food, or varied menu?
e. Would your overall rating of the restaurant be excellent, good, fair, or poor?
ANSWER:
a. Interval
b. Nominal
c. Interval
d. Nominal
e. Ordinal 20 Chapter Two
SECTION 2
MULTIPLE CHOICE QUESTIONS
In the following multiple-choice questions, please circle the correct answer.
30. The best type of chart for comparing two sets of categorical data is a
a. line chart
b. pie chart
c. histogram
d. bar chart
ANSWER: d
31. Which of the following statements about pie charts is false?
a. Pie charts are graphical representations of the relative frequency distribution
b. Pie charts are usually used to display the relative sizes of categories for interval
data.
c. Pie charts always have the shape of a circle
d. Area of each slice of a pie chart is the proportion of the corresponding
category of the frequency distribution of a categorical variable
ANSWER: b
32. The two graphical techniques we usuallyuse to present nominal data are
a. bar chart and histogram
b. pie chart and ogive
c. bar chart and pie chart
d. histogram and ogive
ANSWER: c
33. Which of the following statements is false?
a. A bar chart is similar to a histogram
b. A pie chart is a circle subdivided into slices whose areas are proportional to the
frequencies
c. Pie charts emphasize the frequency of occurrences of each category in a
frequency distribution
d. None of the above
ANSWER: c
34. Which of the following statements is true?
a. Bar charts focus the attention on the frequency of the occurrences of the
categories
b. A bar chart is created by drawing a rectangle representing each category
c. The height of each rectangle in a bar chart represents the frequency for a
particular category
d. Allof the above
ANSWER: d Graphical and Tabular Descriptive Techniques
21
TRUE / FALSE QUESTIONS
35. A bar chart is used to represent interval data.
ANSWER: F
36. One of the advantages of a pie chart is that it clearly shows that the total of all the
categories of the pie adds to 100%.
ANSWER: T
37. The bar chart is preferred to the pie chart, because the human eye can more accurately
judge length comparisons against a fixed scale (as in a bar chart) than angular measures
(as in a pie chart).
ANSWER: T
38. Bar and pie charts are graphical techniques for nominal data. The former focus the
attention on the frequency of the occurrences of the categories, and the later emphasize
the proportion of occurrences of each category.
ANSWER: T
39. Bar and pie charts are two graphical techniques that can be used to represent nominal
data.
ANSWER: T
40. A bar chart is similar to a histogram in the sense that the bases of the rectangles are
arbitrary intervals whose centers are the midpoints of the intervals.
ANSWER: F
41. If we wish to emphasize the relative frequencies for nominal data, we draw a histogram
instead of drawing a bar chart.
ANSWER: F
42. Pie and bar charts are used widelyin newspapers, magazines, and business and
government reports.
ANSWER: T
43. The size of each slice in a pie chart is proportional to the percentage corresponding to that
category.
ANSWER: T
44. A category that contains 30% of the observations is represented by a slice of a pie chart
that contains 100 degrees.
ANSWER: F 22 Chapter Two
STATISTICAL CONCEPTS & APPLIED QUESTIONS
45. Identify the type of data for which each of the following graphs is appropriate.
a. Pie chart
b. Bar chart
ANSWER:
a. Nominal
b. Nominal
46. 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 Democrat, and 3 for
Independent, the data collected were as fol3, 1, 3, 3, 2, 1, 3, 3, 2, 1, 1, 3,
2, 3, 1, 3, 2, 3, 2, 1, 1, and 3. Construct a frequency bar graph.
ANSWER:
12
10
y
n 8
u 6
r 4
F
2
0
RepublicanDemocrat Independent
FOR QUESTIONS 47 AND 48, USE THE FOLLOWING NARRATIVE:
Narrative: Car Dealers
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 M
T C C T U M M C C T
T U C U T M M C U T Graphical and Tabular Descriptive Techniques
23
47. {Car Dealers Narrative} Construct a frequency bar chart.
ANSWER:
15
y
n 10
u
r 5
F
0
C M T U
Dealership
48. {Car Dealers Narrative} Construct a pie chart. Which car dealer offered the best overall
service?
ANSWER:
U
17.5%
C
35.0%
T
22.5%
M
25.0%
It seems that Carriage Motors offered the best overall service. 24 Chapter Two
49. Given the following five categories and the number of times each occurs, draw a pie chart
and a bar chart.
Category 1 2 3 4 5
Frequency 15 30 40 25 20
ANSWER:
Bar Chart
45
40
35
30
c
e25
q
r20
F
15
10
5
0
1 2 3 4 5
Category Graphical and Tabular Descriptive Techniques
25
Pie Chart
5 1
15% 12%
2
4 23%
19%
3
31%
FOR QUESTIONS 50 AND 51, USE THE FOLLOWING NARRATIVE:
Narrative: Business School Graduates
The frequency distribution for a sample of 200 business school graduates is shown in the
following table.
Major of Graduates Number of graduates
Accounting 58
Finance 42
Management 38
Marketing 52
Other 10
50. {Business School Graduates Narrative} Draw a pie chart of the number of graduates.
ANSWER:
Other
5.0%
Accounting
Marketing 29.0%
26.0%
Management Finance
19.0% 21.0% 26 Chapter Two
51. {Business School Graduates Narrative} Draw a frequency bar chart.
ANSWER:
70
60
y 50
n
u 40
e 30
F 20
10
0
g e n g r
t n e et te
on i ge r O
cc F n Ma
A M
Major Graphical and Tabular Descriptive Techniques
27
SECTION 3
MULTIPLE CHOICE QUESTIONS
In the following multiple-choice questions, please circle the correct answer.
52. The most appropriate type of chart for determining the number of observations at or
below a specific value is:
a. a histogram
b. a pie chart
c. a time-series chart
d. a cumulative frequency ogive
ANSWER: d
53. In general, incomes of employees in large firms tend to be
a. positively skewed
b. negatively skewed
c. symmetric
d. Allof the above
ANSWER: a
54. The total area of the bars in a relative frequency histogram:
a. depends on the sample size
b. depends on the number of bars
c. depends on the width of each bar
d. depends on the height of each bar
ANSWER: c
55. Which of the following statements is false?
a. A frequency distribution counts the number of observations that fall into each
of a series on intervals, called classes that cover the complete range of
observations.
b. The intervals in a frequency distribution may overlap to ensure that each
observation is assigned to an interval
c. Although the frequency distribution provides information about how the
numbers in the data set are distributed, the information is more easily
understood and imparted by drawing a histogram
d. The number of class intervals we select in a frequency distribution depends
entirely on the number of observations in the data set
ANSWER: b
56. The total area of the five bars in a relative frequency histogram for which the width of
each bar is four units is:
a. 5
b. 4
c. 9
d. 1 28 Chapter Two
ANSWER: b
57. The relative frequency of a class is computed by
a. dividing the frequency of the class by the number of classes
b. dividing the frequency of the class by the class width
c. dividing the frequency of the class by the total number of observations in the
data set
d. subtracting the lower limit of the class from the upper limit and multiplying the
difference by the number of classes
ANSWER: c
58. A modal class is the class that includes
a. the largest number of observations
b. the smallest number of observations
c. the largest observation in the data set
d. the smallest observation in the data set
ANSWER: a
59. The sum of the relative frequencies for all classes willalways equal
a. the number of classes
b. the class width
c. the total number of observations in the data set
d. one
ANSWER: d
60. When ogives or histograms are constructed, which axis must show the true zero or
“origin”?
a. The horizontal axis.
b. The vertical axis.
c. Both the horizontal and vertical axes.
d. Neither the horizontal nor the vertical axis.
ANSWER: b
61. The width of each bar in a histogram corresponds to the
a. differences between the lower and upper limits of the class.
b. number of observations in each class.
c. midpoint of each class
d. frequency of observations in each class.
ANSWER: a
62. The most important and commonlygraphical presentation of interval data is a
a. bar chart
b. histogram
c. pie chart
d. cumulative frequency distribution
ANSWER: b Graphical and Tabular Descriptive Techniques
29
63. According to Sturges’ rule, the ideal number of class intervals in a frequency distribution
of n = 150 data equals about
a. 8
b. 15
c. 20
d. 28
ANSWER: a
64. According to Sturges’ rule, the ideal number of class intervals in a frequency distribution
equals
a. 5
b. 15
c. 3.3 + log (n), where n is the size of the data set.
d. 1 + 3.3 log (n), where n is the size of the data set.
ANSWER: d
65. How many classes should a histogram contain if the number of observations is 250?
a. 5, 6, or 7
b. 7, 8, or 9
c. 9 or 10
d. 10 or 11
ANSWER: c
66. How many classes should a frequency distribution contain if the number of observations is
45?
a. 5, 6, or 7
b. 7, 8, or 9
c. 9 or 10
d. 10 or 11
ANSWER: a
67. Sturge’s formula recommends that the number of class intervals to construct a frequency
distribution or draw a histogram using a data set with n observations is determined by:
a. log(n)
b. 3.3 log(n)
c. 1 + 3.3 log(n)
d. 2 – 3.3 log(n)
ANSWER: c
68. Which of the following statements about number of modal classes is false?
a. A unimodal histogram is one with a single peak
b. A bimodal histogram is one with two peaks, not necessarilyequal in height
c. A bimodal histogram is one with two peaks equal in height
d. None of the above
ANSWER: c 30 Chapter Two
69. Which of the following statements about shapes of histograms is true?
a. A histogram is said to be symmetric if, when we draw a vertical line down the
center of the histogram, the two sides are identical in shape and size
b. A positively skewed histogram is one with a long tail extending to the right
c. A negatively skewed histogram is one with a long tail extending to the left
d. Allof the above
ANSWER: d Graphical and Tabular Descriptive Techniques
31
TRUE / FALSE QUESTIONS
70. A relative frequency distribution describes the proportion of data values that fall within
each class, and may be presented in a histogram form.
ANSWER: T
71. A relative frequency distribution describes the proportion of data values that fall within
each category.
ANSWER: T
72. The stem-and-leaf display reveals far more information relative to individual values than
does the histogram.
ANSWER: F
73. Individual observations within each class may be found in a frequency distribution.
ANSWER: F
74. The following stem-and-leaf output has been generated by statistical software. The median
of this data is 26.
Stem-and-leaf of C2 N = 75
Leaf Unit = 10
9 0 000112333
14 0 56899
21 1 0000123
26 1 66699
33 2 3334445
(8) 2 66677888
34 3 0023344
27 3 56669999
19 4 000122233
10 4 5556667799
ANSWER: F
75. A cumulative frequency distribution lists the number of observations that are within or
below each of the classes.
ANSWER: T
76. The following stem-and-leaf output has been generated by statistical software. This data
has a negative mode. 32 Chapter Two
Stem-and-leaf of C2 N = 75
Leaf Unit = 0.01
1 -2 6
2 -2 0
5 -1 555
8 -1 420
22 -0 99999887777665
36 -0 44322111111000
(14) 0 01122233333344
25 0 66678889999
14 1 0022222334
4 1 56
2 2 03
ANSWER: T
77. 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
78. A histogram represents nominal data.
ANSWER: F
79. In the term “frequency distribution,” frequency refers to the number of data values falling
within each class.
ANSWER: T
80. The class interval in a frequency distribution is the number of data values falling within
each class.
ANSWER: F
81. 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 willbe 14.
ANSWER: T
82. A stem-and-leaf display describes two - digit integers between 20 and 70. For one of the
classes displayed, the row appears as 4|256. The numerical values being described are 24,
54, and 64.
ANSWER: F
83. The following “character histogram” has been generated by statistical software. The
median class is 150.
Histogram of C1 N = 75 Graphical and Tabular Descriptive Techniques
33
Midpoint Count
-150 1 *
-100 1 *
-50 3 ***
0 2 **
50 7 *******
100 12 ************
150 18 ******************
200 20 ********************
250 5 *****
300 5 *****
350 1 *
ANSWER: T
84. The following stem-and-leaf output has been generated by statistical software. This data
set has a mean that is negative, and there is no modal class.
Stem-and-leaf of C2 N = 10
Leaf Unit = 0.10
2 - 1 53
4 - 0 97
(2) - 0 65
4 0 3
3 0 6
2 1 3
1 1 8
ANSWER: T
85. A frequency distribution is a listing of the individual observations arranged in ascending or
descending order.
ANSWER: F
86. When a distribution has more values to the left and tails to the right, it is skewed
negatively.
ANSWER: F
87. A histogram is said to be symmetric if, when we draw a vertical line down the center of
the histogram, the two sides are identical in shape and size.
ANSWER: T
88. A skewed histogram is one with a long tail extending either to the right or left. The former
is called negatively skewed, and the later is called positivelyskewed. 34 Chapter Two
ANSWER: F
89. A bimodal histogram is one with two or more peaks equal in height.
ANSWER: F
90. A cumulative frequency distribution when presented in graphic form is called an ogive.
ANSWER: T
91. When a distribution has more values to the right and tails to the left, we say it is skewed
positively.
ANSWER: F
92. The sum of relative frequencies in a distribution always equals 1.
ANSWER: T
93. The stem-and-leaf display is often superior to the frequency distribution in that is
maintains the original values for the further analysis.
ANSWER: T
94. The sum of cumulative frequencies in a distribution always equals 1.
ANSWER: F
95. If the values of the sixth and seventh class in a cumulative frequency distribution are the
same, we know that there are no observations in the seventh class.
ANSWER: T
96. The larger the number of observations in a numerical data set, the larger the number of
class intervals needed for a frequency distribution.
ANSWER: T
97. The original data values cannot be assessed once they are grouped into a frequency
distribution.
ANSWER: T
98. A research analyst was directed to arrange raw data collected on the yield of wheat,
ranging from 40 to 90 bushels per acre, in a frequency distribution. He should choose 40
as the class interval width.
ANSWER: F
99. The relative frequency of a class is the frequency of that class divided by the total number
of classes.
ANSWER: F
100. Ogives are plotted at the midpoints of the class intervals.
ANSWER: F Graphical and Tabular Descriptive Techniques
35
101. Sturge’s formula recommends that the number of class intervals needed to draw a
histogram using a data set with 200 observations is 12.79 which we round to 13.
ANSWER: F
102. A modal class is the class with the largest number of observations.
ANSWER: T
103. Incomes of employees in large firms tend to be negatively skewed, because there is a large

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