Chapter 2: Displaying and Describing Categorical Data – Quiz A
Name_____________________________________
A large national retailer of electronics conducted a survey to determine consumer
preferences for various brands of point and shoot digital cameras. The table summarizes
responses by brand and gender.
2.1.3 Create and use frequency and relative frequency distributions and their displays.
1. Identify the variables and tell whether each is categorical or quantitative.
2.1.3 Create and use frequency and relative frequency distributions and their displays.
2. Find each of the following percentages.
a. What percent of the responses were males who prefer Nikon?
b. What percent of the male responses prefer Olympus?
c. What percent of the consumers who choose Nikon were females?
2.3.4 Determine if displays of data are appropriate.
3. What is the marginal distribution of brands?
2.2.4 Determine if displays of data are appropriate.
4. Prepare an appropriate chart to display the marginal distribution of brands.
2.3.4 Determine if displays of data are appropriate.
5. Write a sentence or two about the conditional relative frequency distribution of the
brands among female respondents.
Female Male Total
Cannon Power Shot 73 59 132
Nikon Cool Pix 49 47 96
Sony Cyber Shot 58 33 91
Panasonic Lumix 35 30 65
Fujifilm Finepix 45 28 73
Olympus S/V 37 41 78
Other Brands 86 67 153
Total 383 305 688
2-2 Chapter 2 Displaying and Describing Categorical Data
2.2.1 Determine if displays of data are appropriate.
6. Consider the following side by side bar chart for the data above:
Does the chart indicate that brand preference is independent of gender? Explain.
Quiz A 2-3
Chapter 2: Displaying and Describing Categorical Data – Quiz A – Key
2-4 Chapter 2 Displaying and Describing Categorical Data
Quiz B 2-5
Chapter 2: Displaying and Describing Categorical Data – Quiz B
Name_____________________________________
A full service brokerage firm gathered information on how their clients were investing
for retirement. Based on age, clients were categorized according to where the largest
percentage of their retirement portfolio was invested. The table below summarized the
data.
2.1.3 Create and use frequency and relative frequency distributions and their displays.
1. Identify the variables and tell whether each is categorical or quantitative.
2.1.3 Create and use frequency and relative frequency distributions and their displays.
2. Find each of the following percentages.
a. What percent of the clients are over age 50 who invests in mutual funds?
b. What percent of clients over age 50 invest in mutual funds?
c. What percent of the mutual fund investors are over age 50?
2.3.4 Determine if displays of data are appropriate.
3. What is the marginal distribution of age?
2.2.4 Determine if displays of data are appropriate.
4. Prepare an appropriate chart to display the marginal distribution of age.
2.1.3 Create and use frequency and relative frequency distributions and their displays.
5. Write a sentence or two about the conditional relative frequency distribution of mode
of investment for clients age 50 or younger.
Age 50 or
Younger
Over
Age 50
Total
Mutual Funds 30 34
64
Stocks 37 45
82
Bonds 19 23
42
Total 86 102 188
2-6 Chapter 2 Displaying and Describing Categorical Data
2.4.3 Create and use frequency and relative frequency distributions and their displays.
6. Consider the following side by side bar chart for the data above:
Does the chart indicate that mode of investment is independent of age? Explain.
2.5.4 Create and use frequency and relative frequency distributions and their displays.
7. A newspaper examined the town’s two hospitals and found that over the last six
months at Mercy Hospital 79% of the patients survived while at County Hospital 90%
survived. The table below summarizes the findings.
Lived Died Total % who lived
Mercy Hospital 790 210 1000 79.0%
City Hospital 900 100 1000 90.0%
On closer investigation, it was observed that there was a difference in survival between
patients who were admitted in poor condition or worse compared with patients admitted
in fair condition or better. The following tables were created:
Patients admitted in poor condition or worse:
Lived Died Total % who lived
Mercy Hospital 210 200 410
City Hospital 40 70 110
Investment BondsStocksMutual Funds
OlderYoungerOlderYoungerOlderYounger
60
50
40
30
20
10
0
Dat a
Percent within levels of Investment.
Quiz B 2-7
Patients admitted in fair condition or better:
Lived Died Total % who lived
Mercy Hospital 580 10 590
City Hospital 860 30 890
a) Fill in the four blanks in the two tables above with percentages.
b) Compare the percentages in the first table with those in the next two tables. Do
you observe anything unusual?
c) Which hospital would you choose and why?
2-8 Chapter 2 Displaying and Describing Categorical Data
Chapter 2: Displaying and Describing Categorical Data – Quiz B – Key
Quiz B 2-9
2-10 Chapter 2 Displaying and Describing Categorical Data
Quiz B 2-11
2-12 Chapter 2 Displaying and Describing Categorical Data
Chapter 2: Displaying and Describing Categorical Data– Quiz C – Multiple Choice
Name_____________________________________
2.1.3 Create and use frequency and relative frequency distributions and their displays.
1. A automobile marketing firm conducts a study to see what types of cars people owned before
buying an American car. The results are shown below.
The relative frequency of those who owned Japanese cars previously who now bought American
cars is
A. 59.9 %
B. 29.6%
C. 5.7%
D. 14.9%
E. 2.9%
2.1.3 Examine and use contingency tables.
2. A large national retailer of electronics conducted a survey to determine consumer preferences
for various brands of digital cameras and the data are summarized in the table shown below.
The percentage of consumers who are male and prefer Fujifilm is
A. 44.3 % (305/688).
B. 10.6% (73/688).
C. 38.4% (28/73).
D. 56.2% (41/73).
E. 4.1% (28/688).
Previous Ownership Frequency
American 760
Japanese 375
Korean 72
German 37
Other 24
Total 1268
Female Male Total
Cannon Power Shot 73 59 132
Nikon Cool Pix 49 47 96
Sony Cyber Shot 58 33 91
Panasonic Lumix 35 30 65
Fujifilm Finepix 45 28 73
Olympus S/V 37 41 78
Other Brands 86 67 153
Total 383 305 688
Quiz C 2-13
2.1.3 Examine and use contingency tables.
3. A large national retailer of electronics conducted a survey to determine consumer preferences
for various brands of digital cameras and the data are summarized in the table shown below.
Of the consumers who are male, the percentage who prefer Sony is
A. 44.3 % (305/688).
B. 10.8% (33/305).
C. 36.3% (33/91).
D. 4.8% (33/688).
E. 13.2% (91/688).
2.1.3 Examine and use contingency tables.
4. A large national retailer of electronics conducted a survey to determine consumer preferences
for various brands of digital cameras and the data are summarized in the table shown below. Of
the consumers who prefer Olympus, what percentage is female?
A. 47.4 % (37/78).
B. 6.0% (41/688).
C. 52.6% (41/78).
D. 11.7% (45/383).
E. 11.3% (78/688).
Female Male Total
Cannon Power Shot 73 59 132
Nikon Cool Pix 49 47 96
Sony Cyber Shot 58 33 91
Panasonic Lumix 35 30 65
Fujifilm Finepix 45 28 73
Olympus S/V 37 41 78
Other Brands 86 67 153
Total 383 305 688
Female Male Total
Cannon Power Shot 73 59 132
Nikon Cool Pix 49 47 96
Sony Cyber Shot 58 33 91
Panasonic Lumix 35 30 65
Fujifilm Finepix 45 28 73
Olympus S/V 37 41 78
Other Brands 86 67 153
Total 383 305 688
2-14 Chapter 2 Displaying and Describing Categorical Data
2.2.3 Create and use frequency and relative frequency distributions and their displays.
5. Based on the side-by-side bar chart summarizing consumer preferences for various brands of
digital cameras by gender, which of the following statement(s) are true?
A. It appears that camera preference and gender are at least somewhat related.
B. If Other Brands are ignored, it appears that camera preference and gender are independent.
C. If Other Brands are ignored, it is not obvious that camera preference and gender are
independent.
D. More males than females prefer Cannon.
E. More females than males prefer Sony.
2.2.3 Create and use frequency and relative frequency distributions and their displays.
6. The following is a bar chart summarizing consumer preferences for various brands of digital
cameras.
Quiz C 2-15
This bar chart shows
A. the marginal distribution of brands.
B. the conditional distribution of brands.
C. the contingency distribution of brands.
D. the distribution for a quantitative variable.
E. none of the above.
2.1.4 Find conditional and marginal distributions and make comparisons.
7. A company interested in the health of its employees started a health program including
monitoring blood pressure. Based on age, employees were categorized according to ranges of
blood pressure by age intervals. Data are shown in the table below.
Age
BP Under 30 30-49 Over 50 Total
Low 27 38 31 96
Normal 48 90 92 230
High 23 59 72 154
Total 98 187 195 480
The percentage of employees who are over age 50 and have high blood pressure is
A. 46.8% (72/154).
B. 32.1% (154/480).
C. 31.6% (59/187).
D. 36.9% (72/195).
E. 15.0% (72/480).
2.1.4 Find conditional and marginal distributions and make comparisons.
8. A company interested in the health of its employees started a health program including
monitoring blood pressure. Based on age, employees were categorized according to ranges of
blood pressure by age intervals. Data are shown in the table below.
Age
BP Under 30 30-49 Over 50 Total
Low 27 38 31 96
Normal 48 90 92 230
High 23 59 72 154
Total 98 187 195 480
Of all employees, the percentage who are over 50 and have high blood pressure is
A. 46.8% (72/154).
B. 15.0% (72/480).
C. 31.6% (59/187).
D. 36.9% (72/195).
E. 47.2% (92/195).
2-16 Chapter 2 Displaying and Describing Categorical Data
2.1.4 Find conditional and marginal distributions and make comparisons.
9. A company interested in the health of its employees started a health program including
monitoring blood pressure. Based on age, employees were categorized according to ranges of
blood pressure by age intervals. Data are shown in the table below.
Age
BP Under 30 30-49 Over 50 Total
Low 27 38 31 96
Normal 48 90 92 230
High 23 59 72 154
Total 98 187 195 480
Of all employees, the percentage of those under 50 years old is
A. 17.1% (82/480).
B. 40.6% (195/480).
C. 13.5% (65/480).
D. 36.9% (72/195).
E. 49.4% (285/480).
2.1.4 Find conditional and marginal distributions and make comparisons.
10. A company interested in the health of its employees started a health program including
monitoring blood pressure. Based on age, employees were categorized according to ranges of
blood pressure by age intervals. Data are shown in the table below. .
Age
BP Under 30 30-49 Over 50 Total
Low 27 38 31 96
Normal 48 90 92 230
High 23 59 72 154
Total 98 187 195 480
The percentage of employees with normal or low blood pressure is
A. 67.9% (326/480).
B. 47.9% (230/480).
C. 41.7% (96/230).
D. 80.0% (384/480).
E. 20.0% (96/480).
Quiz C 2-17
2.2.3 Create and use frequency and relative frequency distributions and their displays.
11. Here is a stacked bar chart for data collected about employee blood pressure.
This chart shows
A. the distribution of a quantitative variable.
B. the contingency distribution of blood pressure type.
C. the conditional distribution of blood pressure type.
D. the marginal distribution of blood pressure type.
E. the joint distribution of blood pressure type.
2.5.4 Create and use frequency and relative frequency distributions and their displays.
12. A consulting firm examined the profit of two grocery stores and found that over the last year
at Grocery Store A 66.7% of the months showed profit while at Grocery Store B 83.3% showed
profit. The table below summarizes the findings.
Months
Profit
Months Loss Total % months profit
Grocery A 8 4 12 66.7%
Grocery B 10 2 12 83.3%
On closer investigation, it was observed that there was a difference in profit between stores that
served wealthier neighborhoods versus less wealthy. The following tables were created:
Grocery stores serving wealthy neighborhoods:
Months
Profit
Months Loss Total % months profit
Grocery A 5 3 8 62.5%
Grocery B 5 2 10 50.0%
2-18 Chapter 2 Displaying and Describing Categorical Data
Grocery stores serving less wealthy neighborhoods:
Months
Profit
Months Loss Total % months profit
Grocery A 2 2 4 50.0%
Grocery B 1 1 2 50.0%
What can be assumed about the profit of grocery stores?
A. Grocery Store B has more consistent profit overall.
B. It is clear that less wealthy neighborhoods will not yield these grocery store profits.
C. It is unclear how to predict the profit of these grocery stores based on the wealth of
neighborhoods.
D. Grocery Store A showed less profit overall but showed greater profit in wealthier
neighborhoods.
E. There is no difference in profit overall with grocery stores in either wealthier versus less
wealthy neighborhoods.
Quiz C 2-19
Chapter 2: Displaying and Describing Categorical Data – Quiz C – Key
2-20 Chapter 2 Displaying and Describing Categorical Data
Chapter 2: Displaying and Describing Categorical Data– Quiz D – Multiple Choice
Name_____________________________________
2.1.3 Create and use frequency and relative frequency distributions and their displays.
1. A restaurant uses comment cards to get feedback from its customers about newly
added items to the menu. It recently introduced homemade organic veggie burgers.
Customers who tried the new burger were asked if they would order it again. The data
are summarized in the table below. What percentage of customers would definitely order
the veggie burger again?
A. 10%
B. 15%
C. 20%
D. 40%
E. 77%
2.1.3 Create and use frequency and relative frequency distributions and their displays.
2. A restaurant uses comment cards to get feedback from its customers about newly
added items to the menu. It recently introduced homemade organic veggie burgers.
Customers who tried the new burger were asked if they would order it again. The data
are summarized in the table below. What percentage of customers would most likely or
definitely order the veggie burger again?
Response Frequency
Definitely would. 10
Most likely would. 40
Maybe 12
Definitely would not. 3
A. 10%
B. 15%
C. 40%
D. 50%
E. 77%
Response Frequency
Definitely would. 10
Most likely would. 40
Maybe 12
Definitely would not. 3
Quiz D 2-21
2.2.1 Determine if displays of data are appropriate.
3. A restaurant uses comment cards to get feedback from its customers about newly
added items to the menu. It recently introduced homemade organic veggie burgers.
Customers who tried the new burger were asked if they would order it again. Which of
the following would be an appropriate method for displaying the data shown in the table?
Response Frequency
Definitely would. 10
Most likely would. 40
Maybe 12
Definitely would not. 3
A. Contingency table.
B. Segmented bar chart.
C. Pie chart.
D. Both A and B.
E. Both B and C.
2.2.1 Determine if displays of data are appropriate.
4. In May, 2010, the Pew Research Center for the People & the Press carried out a
national survey to gauge opinion on the Arizona Immigration Law. Responses (Favor,
Oppose, Don’t Know) were examined according to groups defined by political party
affiliation (Democrat, Republican, Independent). Which of the following would be
appropriate for displaying these data?
A. Contingency table.
B. Pie charts.
C. Segmented bar chart.
D. Side by side bar chart.
E. All of the above.
2.1.3 Examine and use contingency tables.
5. A regional survey was carried out to gauge public opinion on the controversial
Arizona Immigration Law (results shown below). How many respondents are
Republican and favor the law?
Response Democrat Republican Independent
Favor 50 93 35
Oppose 85 45 60
Don’t Know 5 7 20
A. 93
B. 45
C. 145
D. 7
E. 85
2-22 Chapter 2 Displaying and Describing Categorical Data
2.2.3 Create and use frequency and relative frequency distributions and their displays.
6. A regional survey was carried out to gauge public opinion on the controversial
Arizona Immigration Law. The results are displayed in the segmented bar chart below.
Which of the following statements is true?
IndependentRepublicanDemocrat
100
80
60
40
20
0
Data
Don‘t Know
Oppose
Favor
Response
Opinion of Arizona Immigration Law by Political Party
Percent within variables.
A. A greater percentage of Republicans oppose the law compared to Democrats.
B. A greater percentage of Republicans oppose the law compared to Independents.
C. Opinion about the law appears to be independent of political party affiliation.
D. A greater percentage of Democrats oppose the law compared to Republicans.
E. The segmented bar chart is not appropriate for these data.
2.1.4 Find conditional and marginal distributions and make comparisons.
7. A regional survey was carried out to gauge public opinion on the controversial
Arizona Immigration Law. Based on the results displayed in the table below, what
percent of respondents is Independent?
Response Democrat Republican Independent
Favor 50 93 35
Oppose 85 45 60
Don’t Know 5 7 20
A. 35%
B. 9%
C. 29%
D. 45%
E. 25%
Quiz D 2-23
2.1.4 Find conditional and marginal distributions and make comparisons.
8. A regional survey was carried out to gauge public opinion on the controversial
Arizona Immigration Law (results shown below). What percent oppose the law?
Response Democrat Republican Independent
Favor 50 93 35
Oppose 85 45 60
Don’t Know 5 7 20
A. 48%
B. 45%
C. 32%
D. 25%
E. 61%
2.1.4 Find conditional and marginal distributions and make comparisons.
9. A regional survey was carried out to gauge public opinion on the controversial
Arizona Immigration Law (results shown below). Of respondents who are Democrat,
what percent oppose the law?
Response Democrat Republican Independent
Favor 50 93 35
Oppose 85 45 60
Don’t Know 5 7 20
A. 13%
B. 35%
C. 22%
D. 45%
E. 61%
2.1.4 Find conditional and marginal distributions and make comparisons.
10. A regional survey was carried out to gauge public opinion on the controversial
Arizona Immigration Law (results shown below). Of respondents who oppose the law,
what percent is Democrat?
Response Democrat Republican Independent
Favor 50 93 35
Oppose 85 45 60
Don’t Know 5 7 20
A. 13%
B. 35%
C. 22%
D. 45%
E. 6
2-24 Chapter 2 Displaying and Describing Categorical Data
Chapter 2: Displaying and Describing Categorical Data – Quiz D – Key
Quiz E 2-25
Chapter 2: Displaying and Describing Categorical Data– Quiz E – Multiple Choice
Name_____________________________________
2.1.3 Create and use frequency and relative frequency distributions and their displays.
1. A clothing store uses comment cards to get feedback from its customers about newly
added items. It recently introduced plus size fashion wear. Customers who purchased
the items were asked to fill out an online comment survey giving 10% off the next
purchase. The data are summarized in the table below. What percentage of customers
were at least satisfied with the item(s) purchased (Satisfied or Very satisfied)?
A. 49.2%
B. 73.8%
C. 24.6%
D. 26.2%
E. 68.9%
2.1.3 Create and use frequency and relative frequency distributions and their displays.
2. A clothing store uses comment cards to get feedback from its customers about newly
added items. It recently introduced plus size fashion wear. Customers who purchased
the items were asked to fill out an online comment survey giving 10% off the next
purchase. The data are summarized in the table below. What percentage of customers
would be less likely to purchase another item (Less or Not fully satisfied)?
Response Frequency
Very satisfied. 15
Satisfied. 30
Less than fully satisfied. 12
Not satisfied. 4
A. 10%
B. 15%
C. 40%
D. 50%
E. 77%
Response Frequency
Very satisfied. 15
Satisfied. 30
Less than fully satisfied. 12
Not satisfied. 4
2-26 Chapter 2 Displaying and Describing Categorical Data
2.2.1 Determine if displays of data are appropriate.
3. A clothing store uses comment cards to get feedback from its customers about newly
added items. It recently introduced plus size fashion wear. Customers who purchased
the items were asked to fill out an online comment survey giving 10% off the next
purchase. The data are summarized in the table below. Which of the following would be
an appropriate method for displaying the data shown in the table?
Response Frequency
Very satisfied. 15
Satisfied. 30
Less than fully satisfied. 12
Not satisfied. 4
A. Contingency table.
B. Segmented bar chart.
C. Pie chart.
D. Both A and B.
E. Both B and C.
2.2.1 Determine if displays of data are appropriate.
4. Accenture, a consulting firm, conducted an online survey of 500 US consumers in
September 2013. Based on their response to the question “What is your motive for
shopping late in the season?” which of the following would be an appropriate method for
displaying the data shown in the table?
A. Contingency table.
B. Pie charts.
C. Segmented bar chart.
D. Side by side bar chart.
E. All of the above.
Response Male Female
Too busy to shop earlier 115 75
More time to save for gifts 50 80
Better discounts available 65 20
Part of the holiday tradition 15 5
None of the above 120 60
Quiz E 2-27
2.3. Examine a contingency table.
5. Accenture, a consulting firm, conducted an online survey of 500 US consumers from
2009 to 2013. The results are displayed in the segmented bar chart below. How many
respondents in 2012 are at least somewhat likely to shop on “Black Friday”?
A. 265
B. 275
C. 140
D. 230
E. 95
2.2. Determine if a display of data is appropriate.
6. Accenture, a consulting firm, conducted an online survey of 500 US consumers from
2009 to 2013. The results are displayed in the segmented bar chart below. Which of the
following statement(s) is (are) true?
A. A smaller percentage of shoppers over the past 5 years are undecided about shopping
on “Black Friday”.
B. In 2013, there was an increase in Very likely to shop on “Black Friday” over 2012.
C. From 2011 to 2013, there was a decrease in Not at all likely to shop on “Black
Friday”.
D. A greater percentage of shoppers over the past 5 years are at least somewhat likely to
shop on “Black Friday”.
E. The segmented bar chart is not appropriate for these data.
2-28 Chapter 2 Displaying and Describing Categorical Data
2.1.4 Find conditional and marginal distributions and make comparisons.
7. Accenture, a consulting firm, conducted an online survey of 500 US consumers from
in 2013.
What percentage of men were felt that better discounts were available on “Black Friday”?
A. 26.5%
B. 65%
C. 20%
D. 17.8%
E. 5.5%
Response Male Female
Too busy to shop earlier 115 75
More time to save for gifts 50 80
Better discounts available 65 20
Part of the holiday tradition 15 5
None of the above 120 60
Quiz E 2-29
2.1.4 Find conditional and marginal distributions and make comparisons.
8. Accenture, a consulting firm, conducted an online survey of 500 US consumers from
in 2013.
What percentage of those who thought that better discounts were available on “Black
Friday” were female?
A. 81.3%
B. 33.3%
C. 11.1%
D. 47.2%
E. 23.5%
2.1.4 Find conditional and marginal distributions and make comparisons.
9. Accenture, a consulting firm, conducted an online survey of 500 US consumers in
September 2013. Based on their response to the question “What is your motive for
shopping late in the season?” which of the following would be appropriate method(s) for
displaying the male only data shown in the table?
A. Contingency table.
B. Pie chart.
C. Segmented bar chart.
D. Side by side bar chart.
E. All of the above.
Response Male Female
Too busy to shop earlier 115 75
More time to save for gifts 50 80
Better discounts available 65 20
Part of the holiday tradition 15 5
None of the above 120 60
Response Male Female
Too busy to shop earlier 115 75
More time to save for gifts 50 80
Better discounts available 65 20
Part of the holiday tradition 15 5
None of the above 120 60
2-30 Chapter 2 Displaying and Describing Categorical Data
2.1.4 Find conditional and marginal distributions and make comparisons.
10. Accenture, a consulting firm, conducted an online survey of 500 US consumers in
September, 2013.
What percentage of consumers thought that shopping on “Black Friday” is part of the
holiday tradition?
A. 8.3%
B. 33.3%
C. 11.1%
D. 12.5%
E. 75.0%
Response Male Female
Too busy to shop earlier 115 75
More time to save for gifts 50 80
Better discounts available 65 20
Part of the holiday tradition 15 5
None of the above 120 60
Quiz E 2-31
Chapter 2: Displaying and Describing Categorical Data – Quiz E – Key