CHAPTER 2
DESCRIBING DATA: GRAPHS AND TABLES
MULTIPLE CHOICE QUESTIONS
In the following multiple-choice questions, please circle the correct answer.
1.
Data that arise from counts are called:
a. continuous
b. nominal
c. counted
d. discrete
ANSWER: d
2.
A sample of a population taken at one particular point in time is categorized as:
a. categorical
b. discrete
c. cross-sectional
d. time-series
ANSWER: c
3.
Gender and State are examples of which type of data?
a. Discrete
b. Continuous
c. Categorical
d. Ordinal
ANSWER: c
6
Describing Data: Graphs and Tables
4.
A histogram that is positively skewed is:
a. skewed to the right
b. skewed to the left
c. balanced
d. symmetric
ANSWER: a
5.
A histogram that has exactly two peaks is called a
distribution.
a. unimodal
b. bimodal
c. skewed
d. scatter
ANSWER: b
6.
An opinion variable expressed numerically on a 1-5 scale is a(n):
a. histogram
b. opinion poll
c. categorical scale
d. Likert scale
ANSWER: d
7.
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 arises from continuous measurements
d. we track the variable through a period of time
ANSWER: a
8.
A population includes:
a. only people
b. only households
c. all objects of interest in a particular study
d. only machines
ANSWER: c
7
Chapter 2
9.
Researchers try to gain insight into the characteristics of a population by
examining a __________ of the population.
a. model
b. sample
c. description
d. replica
ANSWER: b
10.
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
11.
The tool that provides useful information about a data set by breaking it down into
subpopulations is:
a. the histogram
b. the scatterplot
c. the pivot table
d. the spreadsheet
ANSWER: c
12.
The tables that result from pivot tables are called:
a. samples
b. sub-tables
c. specimens
d. crosstabs
ANSWER: d
13.
In order for the characteristics of a sample to be generalized to the entire
population, it should be ________________ of the population.
a. symbolic
b. typical
c. representative
d. illustrative
ANSWER: c
8
Describing Data: Graphs and Tables
14.
A bimodal histogram is often an indication that:
a. the data are incorrect
b. the data are inconclusive
c. the sample is not representative of the population
d. the data come from two or more distinct populations
ANSWER: d
15.
The Literary Digest fiasco of 1936 is an example of:
a. a sample that is not representative of its population
b. an incomplete population
c. an inconclusive data set
d. a symmetric histogram
ANSWER: a
16.
A _________________ indicates how many observations fall into various
categories.
a. Likert scale
b. frequency table
c. sample table
d. tabulation scale
ANSWER: b
17.
A _________________ is the graphical analog of a frequency table.
a. histogram
b. graph
c. diagram
d. table
ANSWER: a
18.
A histogram that has a single peak and looks approximately the same to the left
and right of the peak is:
a. bimodal
b. symmetric
c. balanced
d. proportional
ANSWER: b
9
Chapter 2
19.
An observation is a:
a. variable
b. field
c. member of a population or sample
d. characteristic of a population
ANSWER: c
20.
If data is stored in a database package, which of the following terms are typically
used?
a. Fields and records
b. Cases and columns
c. Variables and samples
d. Variables and observations
ANSWER: a
21.
A scatterplot allows one to see:
a. whether there is any relationship between two variables
b. what type of relationship there is between two variables
c. both a and b
d. neither a nor b
ANSWER: c
22.
A time series plot is essentially a:
a. histogram
b. scatterplot
c. diagram
d. figure
ANSWER: b
23.
The commonly observed shapes of histograms are:
I. symmetric
II. asymmetric
III. bimodal
IV. polymodal
V. positively skewed
VI. negatively skewed
a. I, II, III and IV
b. III, IV, V, and VI
c. II, III, IV, and V
d. I, III, V, and VI
ANSWER: d
10
Describing Data: Graphs and Tables
24.
When we look at a time series plot, we usually look for which two things?
a. “Is there an observable trend?” and “Is there a seasonal pattern?”
b. “Is there an observable trend” and “Can we make predictions?”
c. “Is the sample representative?” and “Is there a seasonal pattern?”
d. “Is there an observable trend?” and “Is the trend symmetric?”
ANSWER: a
11
Chapter 2
TEST QUESTIONS
25.
The students at small community college in Iowa apply to study either English or
business. Some administrators at the college are concerned that women are being
discriminated against in being allowed admittance, particularly in the business
program. Below, you will find two pivot tables that show the percentage of
students admitted by gender to the English program and the business school. The
data has also been presented graphically. What do the data and graphs indicate?
Gender
Female
Male
Total
English program
No
Yes
Total
46.0% 54.0% 100%
60.8% 39.2% 100%
53.5% 46.5% 100%
Gender
Female
Male
Total
Female
Male
80.0%
60.0%
60.0%
40.0%
40.0%
20.0%
20.0%
Female
Male
M
0.0%
al
m
Fe
Yes
e
al
No
e
e
al
m
Yes
Fe
No
e
al
M
0.0%
Total
100%
100%
100%
Percent of Business Students
Admitted
Percent Admitted by Gender
80.0%
Business school
No
Yes
69.2% 30.8%
64.1% 35.9%
65.4% 34.6%
ANSWER:
These data indicate that a smaller percentage of women are being admitted to the
business program. Only 30.8% of women are being admitted to the business
program compared to 35.9% for men. However, it is also important to note that
only 34.6% of all applicants (women and men) are admitted to the business
program compared to 46.5% for the English program. Maybe the males should
say something about being discriminated against in being admitted to the English
program.
26.
A sample of 30 schools produced the pivot table shown below for the average
percentage of students graduating from high school. Use this table to determine
how the type of school (public or Catholic) that students attend affects their
chance of graduating from high school.
12
Describing Data: Graphs and Tables
ANSWER:
The percentages in the right column suggest that if we look at all schools, the rate
of graduation is much higher in Catholic schools than in public schools. But a
look at the breakdowns in the three ethnic group columns shows that this
difference is due primarily to schools that are black and Latino. There isn't much
difference in graduation rates between Catholic and public schools that are white.
27.
The data below represents monthly sales for two years of beanbag animals at a
local retail store (Month 1 represents January and Month 12 represents
December). Given the time series plot below, do you see any obvious patterns in
the data? Explain.
Time series chart of Sales
525
Sales
450
375
300
225
150
75
1
2 3
4 5
6 7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Observation Number
ANSWER:
This is a representation of seasonal data. There seems to be a small increase in
months 3, 4, and 5 and a large increase at the end of the year. The sales of this
item seem to peak in December and have a significant drop off in January.
28.
A data set from a sample of 399 Michigan families was collected. The
characteristics of the data include family size (large or small), number of cars
owned by family (1, 2, 3, or 4), and whether family owns a foreign car. Excel
produced the pivot table shown below.
13
Chapter 2
Use this pivot table to determine how family size and number of cars owned
influence the likelihood that a family owns a foreign car.
ANSWER:
The pivot table shows that the more cars a family owns, the more likely it is that
they own a foreign car (makes sense!). Also, the percentage of large families who
own a foreign car is larger than the similar percentage of small families (36.0%
versus 10.4%).
29.
An operations management professor is interested in how her students performed
on her midterm exam. The data and histogram are presented below. The
histogram represents the distribution of exam scores (where the maximum score is
100) for 50 students.
Student
1
2
3
4
5
6
7
8
9
10
11
12
13
Score
72
95
83
85
65
82
84
74
74
82
81
75
78
Student
14
15
16
17
18
19
20
21
22
23
24
25
26
Score
78
72
73
75
79
80
87
80
91
74
69
88
84
Student
27
28
29
30
31
32
33
34
35
36
37
38
39
Score
83
87
82
72
97
88
70
83
92
94
63
83
81
Student
40
41
42
43
44
45
46
47
48
49
50
Score
84
78
84
71
77
78
70
86
67
91
78
Histogram for Score
20
18
16
14
12
10
8
6
4
2
0
<=70
70- 80
80- 90
>90
Category
Based on this histogram, how would you characterize the students’ performance
on this exam?
ANSWER:
Exam scores are fairly normally distributed. Majority of scores (76%) are
between 70 and 90 points, while 12% of scores are above 90 and 12% of scores
are 70 or below.
14
Describing Data: Graphs and Tables
30.
A health magazine reported that a man’s weight at birth has a significant impact
on the chance that the man will suffer a heart attack during his life. A statistician
analyzed a data set for a sample of 798 men, and produced the pivot table and
histogram shown below. Determine how birth weight influences the chances that
a man will have a heart attack.
Percentage of men with heart attack
60.00%
50.00%
40.00%
30.00%
20.00%
10.00%
0.00%
5-5.5
5.5-6
6-6.5
6.5-7
7-7.5
7.5-8
8-8.5
8.5-9
Birth weight
ANSWER:
The above pivot table shows counts (as percentages of row) of heart attack versus
birth weight, where birth weight has been grouped into categories. The
percentages in each category with heart attacks have then been plotted versus
weight at birth as shown in the histogram. It appears that the likelihood of a heart
attack is greatest for light babies, and then decreases steadily, but increases
slightly for the heaviest babies.
15
Chapter 2
31.
The table shown below contains information technology (IT) investment as a
percentage of total investment for eight countries during the 1990s. It also
contains the average annual percentage change in employment during the 1990s.
Explain how these data shed light on the question of whether IT investment
creates or costs jobs.
1990s
Country for eight countries
% IT during the
% Change
Netherlands
2.5%
1.6%
Italy
4.1%
2.2%
Germany
4.5%
2.0%
France
5.5%
1.8%
Canada
8.3%
2.7%
Japan
8.3%
2.7%
Britain
8.3%
3.3%
U.S.
12.4%
3.7%
ANSWER:
4.0%
Percentage Change
Correlation = 0.9301
3.5%
There is a clear and surprisingly consistent upward
3.0%
trend in these data -- t he larger the IT investment
percentage, the larger the percentage increase in
employment (at least among these 8 countries).
2.5%
2.0%
1.5%
1.0%
0.5%
0.0%
0.0%
2.0%
4.0%
6.0%
IT Percentage
16
8.0%
10.0%
12.0%
Describing Data: Graphs and Tables
QUESTIONS 32 THROUGH 35 ARE BASED ON THE FOLLOWING INFORMATION:
A real estate agent has gathered information on 40 houses that were recently sold in a
local community. The data below represents the following variables: the selling price of
each house (in thousands of dollars), the appraised value of each house (in thousands of
dollars), the size of the house (in hundreds of square feet), and the number of bedrooms.
House
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
Value
121.87
122.78
144.35
116.20
139.49
144.80
107.06
147.47
135.12
140.24
129.89
121.14
157.79
135.57
151.99
120.53
118.64
149.51
146.86
152.84
122.27
145.71
138.38
109.46
144.68
133.27
133.27
150.38
135.26
112.60
114.23
153.24
125.89
135.62
121.45
132.45
135.83
125.76
125.84
135.32
Price
119.37
130.39
135.70
126.30
137.08
139.53
114.34
140.04
136.01
140.93
132.42
118.30
155.55
128.50
143.36
119.65
122.57
145.27
149.73
156.13
126.72
141.13
136.53
118.04
153.70
126.31
134.02
141.56
142.96
118.53
121.59
146.40
141.25
130.73
115.97
125.21
130.37
119.75
120.93
126.80
17
Sq. Footage
20.5
15.9
18.6
12.1
17.1
17.2
16.7
16.5
16.1
15.7
16.5
16.4
22.7
19.7
18.2
16.5
14.7
18.5
21.7
19.6
19.2
18.5
14.3
13.9
21.3
18.9
16.4
20.7
18.1
14.6
14.1
21.9
15.8
18.4
16.3
15.8
17.6
18.1
17.1
18.9
# of Bedrooms
4
3
3
2
3
3
3
3
2
3
4
3
5
4
3
3
2
4
4
3
4
3
2
2
4
4
2
3
3
2
2
4
3
3
2
3
3
4
3
3
Chapter 2
32.
Indicate whether each of the four variables is continuous or discrete.
ANSWER:
Value – continuous
Price – continuous
Square Footage – continuous
Number of Bedrooms – discrete
33.
The histograms for both the appraised values and selling prices are presented
below. In what ways are the two distributions similar? In what ways are they
different?
Histogram for Value
12
10
8
6
4
2
0
<=120
120- 130
130- 140
140- 150
>150
Category
Histogram for Price
12
10
8
6
4
2
0
<=120
120- 130
130- 140
140- 150
>150
Category
ANSWER:
Both distributions seem to center around $130,000 - $140,000. The selling price
appears to be slightly higher than the appraisal value.
18
Describing Data: Graphs and Tables
34.
The following scatterplot compares the selling price and the appraised value.
Correlation = 0.877
157.5
150.0
Value
142.5
135.0
127.5
120.0
112.5
100
110
120
130
140
150
160
Price
Is there a linear relationship between these two variables? If so, how would you
characterize the relationship?
ANSWER:
Yes, there is a linear relationship. Correlation value = 0.877 represents a rather
strong relationship. You can also see from the scatterplot, that there is a positive
relationship between the selling price and the appraisal value.
The two scatterplots below use the same home sales data presented above. The
first chart shows the relationship between the size of the home and the selling
price. The second chart examines the relationship between the number of
bedrooms in the home and its selling price. Which of these two variables (the size
of the home or the number of bedrooms) seems to have the stronger relationship
with the home’s selling price? Justify your answer.
Correlation = 0.657
160
150
140
Price
35.
130
120
110
100
12
14
16
18
Square Footage
19
20
22
24
Chapter 2
Correlation = 0.452
160
150
Price
140
130
120
110
100
2.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
Number of Bedrooms
ANSWER:
The relationship between selling price and house size (in square feet) seems to be
a stronger relationship. The correlation value is higher for house size (0.657 to
0.452). The house size and the number of bedrooms seem to be closely related,
but the house size variable seems to offer more information. The number of
bedrooms is a discrete variable.
QUESTIONS 36 THROUGH 42 ARE BASED ON THE FOLLOWING INFORMATION:
A recent survey data collected from 1000 randomly selected Internet users. The
characteristics of the users include their gender, age, education, marital status and annual
income. Using Excel, the following pivot tables were produced.
20
Describing Data: Graphs and Tables
36.
What percentage of these Internet users are men under the age of 30?
ANSWER:
Approximately 19% of these Internet users are men under the age of 30.
37.
What percentage of these Internet users are single with no formal education
beyond high school?
ANSWER:
Approximately 16% of these Internet users are single with no formal education
beyond high school.
38.
What percentage of these Internet users are currently employed?
ANSWER:
Approximately 77% of these Internet users are currently employed.
39.
What is the average salary of the employed Internet users in this sample?
ANSWER:
The average salary of employed Internet users in this sample is about $60,564.
40.
What percentage of these Internet users are married with formal education beyond
high school?
ANSWER:
Approximately 37% of these Internet users are married with formal education
beyond high school?
41.
What percentage of these Internet users are married?
ANSWER:
Approximately 69% of these Internet users are married.
21
Chapter 2
42.
What percentage of these Internet users are in the 58-71 age group?
ANSWER:
Approximately 9% of these Internet users are in the 58-71 age group.
QUESTIONS 43 THROUGH 45 ARE BASED ON THE FOLLOWING INFORMATION:
Below you will find current annual salary data and related information for 30 employees
at Gamma Technologies, Inc. These data include each selected employees gender (0 =
male, 1 = female), age, number of years of relevant work experience prior to employment
at Gamma, number of years of employment at Gamma, the number of years of postsecondary education, and annual salary.
Gamma Technologies, Inc. Employee Salary Structure
Gender
Age
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
39
44
24
25
56
41
33
37
51
23
36
58
31
21
47
35
52
29
42
60
50
33
26
38
44
25
37
53
46
20
Prior
Experience
5
12
0
2
5
9
6
11
12
0
5
9
1
0
5
3
12
3
11
10
8
1
0
6
7
0
8
13
7
0
Gamma
Experience
12
8
2
1
24
10
2
6
16
1
5
22
1
1
16
7
14
3
7
21
13
2
5
6
12
3
5
13
18
1
22
Education
4
6
4
4
8
4
6
4
6
4
6
4
6
2
4
4
8
2
4
4
4
6
2
6
4
4
4
6
4
0
Annual
Salary
$37,500
$50,912
$29,356
$27,750
$97,844
$48,442
$40,207
$42,331
$87,489
$26,118
$40,025
$88,763
$35,829
$17,784
$54,199
$36,932
$93,278
$22,100
$49,987
$85,471
$52,220
$36,109
$23,105
$39,455
$49,861
$30,327
$31,008
$90,874
$57,966
$16,500
Describing Data: Graphs and Tables
43.
Indicate the type of data for each of the six variables included in this set.
ANSWER:
Gender – categorical, nominal
Age – numerical, continuous
Prior experience – numerical, discrete
Gamma experience – numerical, discrete
Education – numerical, discrete
Annual salary – numerical, continuous
44.
Based on the histogram shown below, how would you describe the age distribution
for these data?
Histogram for Age
10
9
8
7
6
5
4
3
2
1
0
<=20
20- 30
30- 40
40- 50
>50
Category
ANSWER:
The age distribution is skewed slightly to the right. Largest grouping is in the 3040 range. This means that most workers are above the age of 30 years and only
one worker is 20 years old or younger.
45.
Based on the histogram shown below, how would you describe the salary
distribution for these data?
Histogram for Annual Salary
8
7
6
5
4
3
2
1
0
<=20000
2000030000
3000040000
4000050000
5000060000
Category
23
6000070000
7000080000
8000090000
>90000
Chapter 2
ANSWER:
The salary distribution is skewed to the right. There appears to be several workers
who are being paid substantially more than the others. If you eliminate those
above $80,000, the salaries are fairly normally distributed around $35,000.
QUESTIONS 46 THROUGH 55 ARE BASED ON THE FOLLOWING INFORMATION:
A sample of 150 students at a State University was taken after the final business statistics
exam to ask them whether they went partying the weekend before the final or spent the
weekend studying, and whether they did well or poorly on the final. The following table
contains the result.
Studying for Exam
Went Partying
46.
Did Well in Exam
60
22
Did Poorly in Exam
15
53
Of those in the sample who went parting the weekend before the final exam, what
percentage of them did well in the exam?
ANSWER:
22 out of 75, or 29.33%
47.
Of those in the sample who did well on the final exam, what percentage of them
went partying the weekend before the exam?
ANSWER:
22 out of 82, or 26.83%
48.
What percentage of the students in the sample went partying the weekend before
the final exam and did well in the exam?
ANSWER:
22 out of 150, or 14.67%
49.
What percentage of the students in the sample spent the weekend studying and did
well in the final exam?
ANSWER:
60 out of 150, or 40%
24
Describing Data: Graphs and Tables
50.
What percentage of the students in the sample went partying the weekend before
the final exam and did poorly on the exam?
ANSWER:
53 out of 150, or 35.33%
51.
If the sample is a good representation of the population, what percentage of the
students in the population should we expect to spend the weekend studying and
do poorly on the final exam?
ANSWER:
15 out of 150, or 10%
52.
If the sample is a good representation of the population, what percentage of those
who spent the weekend studying should we expect to do poorly on the final
exam?
ANSWER:
15 out of 75, or 20%
53.
If the sample is a good representation of the population, what percentage of those
who did poorly on the final exam should we expect to have spent the weekend
studying?
ANSWER:
15 out of 68, or 22.06%
54.
Of those in the sample who went parting the weekend before the final exam, what
percentage of them did poorly in the exam?
ANSWER:
53 out of 75, or 70.67%
55.
Of those in the sample who did well in the final exam, what percentage of them
spent the weekend before the exam studying?
ANSWER:
60 out of 82, or 73.17%
25
Chapter 2
QUESTIONS 56 THROUGH 63 ARE BASED ON THE FOLLOWING INFORMATION:
The histogram below represents scores achieved by 250 job applicants on a personality
profile.
Relative Frequency
0.30
0.20
0.20
0.20
0.20
0.10
0.10
0.10
0.10
0.10
0.00
0
56.
10
20
30
40
50
What percentage of the job applicants scored between 30 and 40?
ANSWER:
10%
57.
What percentage of the job applicants scored below 60?
ANSWER:
90%
58.
How many job applicants scored between 10 and 30?
ANSWER:
100
59.
60
How many job applicants scored above 50?
ANSWER:
50
26
70
Describing Data: Graphs and Tables
60.
Seventy percent of the job applicants scored above what value?
ANSWER:
20
61.
Half of the job applicants scored below what value?
ANSWER:
30
62.
What percentage of the applicants scored at most 50?
ANSWER:
80%
63.
How many applicants scored between 10 and 50?
ANSWER:
175
27
Chapter 2
TRUE / FALSE QUESTIONS
64.
A frequency table indicates how many observations fall within each category, and
a histogram is its graphical analog.
ANSWER:
65.
Individual observations within each category may be found in a frequency table.
ANSWER:
66.
T
Data can be categorized as cross-sectional or time series.
ANSWER:
73.
T
Categorical variables can be coded numerically or left uncoded.
ANSWER:
72.
F
Age, height, and weight are examples of numerical data.
ANSWER:
71.
T
A variable is some characteristic of a population, while data are the observed
values of a variable based on a sample.
ANSWER:
70.
F
Both ordinal and nominal variables are categorical.
ANSWER:
69.
T
A frequency table is a listing of the individual observations arranged in ascending
or descending order.
ANSWER:
68.
F
In the term “frequency table,” frequency refers to the number of data values
falling within each category.
ANSWER:
67.
T
T
All nominal data may be treated as ordinal data.
ANSWER:
F
28
Describing Data: Graphs and Tables
74.
Four different shapes of histograms are commonly observed: symmetric,
positively skewed, negatively skewed, and bimodal.
ANSWER:
75.
A histogram is skewed to the right (or positively skewed) if it has a single peak
and the values of the distribution extend much further to the left of the peak than
to the right of the peak.
ANSWER:
76.
F
Creating a histogram can be a tedious task, but an add-in such as StatPro makes it
relatively easy. However, you must be prepared to specify the categories.
ANSWER:
82.
T
A bimodal histogram is one with two peaks equal in height.
ANSWER:
81.
F
Some histograms have two or more peaks. This is often an indication that the data
come from two or more distinct populations.
ANSWER:
80.
T
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 positively skewed.
ANSWER:
79.
F
A histogram is said to be symmetric if it has a single peak and looks
approximately the same to the left and right of the peak.
ANSWER:
78.
F
A histogram is skewed to the left (or negatively skewed) if it has a single peak
and the values of the distribution extend much further to the right of the peak than
to the left of the peak.
ANSWER:
77.
T
T
The scatterplot is a graphical technique used to describe the relationship between
two numerical variables.
ANSWER:
T
29
Chapter 2
83.
If we draw a straight line through the points in a scatterplot and most of the points
fall close to the line, we say that there is a strong positive linear relationship
between the two variables.
ANSWER:
84.
Time series data are often graphically depicted on a line chart, which is a plot of
the variable of interest over time.
ANSWER:
85.
T
A variable (or field) is an attribute, or measurement, on members of a population,
whereas an observation (or case or record) is a list of all variable values for a
single member of a population.
ANSWER:
91.
T
A population includes all elements or objects of interest in a study, whereas a
sample is a subset of the population used to gain insights into the characteristics
of the population.
ANSWER:
90.
F
The number of car insurance policy holders is an example of a discrete random
variable
ANSWER:
89.
F
The time required to drive from Iowa City to Lansing is an example of a discrete
random variable.
ANSWER:
88.
T
Numerical variables usually represent membership in groups or categories.
ANSWER:
87.
T
Statisticians often refer to the pivot tables as contingency tables or crosstabs.
ANSWER:
86.
F
T
A variable is usually listed in a row; an observation is usually listed in a column.
ANSWER:
F
30
Describing Data: Graphs and Tables
92.
Phone numbers, Social Security numbers, and zip codes are examples of
numerical variables.
ANSWER:
93.
F
Cross-sectional data are data on a population at a distinct point in time, whereas
time series data are data collected across time.
ANSWER:
T
31