Deck 4: Displaying and Describing Categorical Data

Question 1

Consider the following to answer the question(s) below:
A large national retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender.

Of the consumers who prefer Pentax, what percentage is male?

A) 44.1% (275/623)
B) 6.6% (41/623)
C) 52.6% (41/78)
D) 14.9% (41/275)
E) 12.5% (78/623)

Answer 1

C

Question 2

Consider the following side-by-side bar chart for the data below: Does the chart indicate that mode of investment is independent of age? Explain.

Answer 2

The way clients invest for retirement does seem to be independent of age. These data provide little indication of a difference in mode of investing for retirement based on clients' ages at this firm.

Question 3

Write a sentence or two about the conditional relative frequency distribution of mode of investment for clients age 50 or younger.

Answer 3

Among clients age 50 or younger, 34.9% invest in mutual funds, 43.0% invest in stocks, while 22.1% invest in bonds.

Question 4

What is the marginal distribution of age?

Question 5

Consider the following to answer the question(s) below:
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 and shown in the table below.

The percentage of clients who are over age 50 and invest in mutual funds is

A) 53.1% (34/64)
B) 33.3% (34/102)
C) 18.1% (34/188)
D) 34.0% (64/188)
E) 54.3% (102/188)

Question 6

Consider the following to answer the question(s) below:
A large national retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender.

The percentage of consumers who are male and prefer Pentax is

A) 44.1% (275/623)
B) 6.6% (41/623)
C) 52.6% (41/78)
D) 14.9% (41/275)
E) 12.5% (78/623)

Question 7

Consider the following to answer the question(s) below:
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.

Find each of the following percentages.
a. What percentage of the clients who invest in mutual funds are over age 50?
b. What percentage of clients over age 50 invest in mutual funds?
c. What percentage of the mutual fund investors are over age 50?

Question 8

Consider the following to answer the question(s) below:
A large national retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender.

Find each of the following percentages.
a. What percentage of the responses were males who prefer Pentax?
b. What percentage of the male responses prefer Pentax?
c. What percentage of the consumers who chose Pentax were males?

Question 9

What is the marginal distribution of brands?

Question 10

Prepare an appropriate chart to display the marginal distribution of brands.

Question 11

Here is the side-by-side bar chart for these data. Which of the following statements is true?

A) It appears that camera preference and gender are not related.
B) It appears that camera preference and gender are not independent.
C) It appears that camera preference and gender are independent.
D) More males than females prefer Cannon.
E) More females than males prefer Pentax.

Question 12

Consider the following side-by-side bar chart for the data: Does the chart indicate that brand preference is independent of gender? Explain.

Question 13

Consider the following to answer the question(s) below:
A large national retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender.

Identify the variables and tell whether each is categorical or quantitative.

Question 14

Write a sentence or two about the conditional relative frequency distribution of the brands among female respondents.

Question 15

Consider the following to answer the question(s) below:
A large national retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender.

Of the consumers who are male, the percentage who prefer Pentax is

A) 44.1% (275/623)
B) 6.6% (41/623)
C) 52.6% (41/78)
D) 14.9% (41/275)
E) 12.5% (78/623)

Question 16

Consider the following to answer the question(s) below:
A large national retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender.

Of the consumers who prefer Canon, what percentage is female?

A) 63.74% (58/91)
B) 16.67% (58/348)
C) 9.31% (58/623)
D) 14.61% (91/623)
E) 55.86% (348/623)

Question 17

The following bar chart for these data shows

A) the marginal distribution of brands
B) the conditional distribution of brands
C) the marginal distribution of gender
D) the conditional distribution of gender
E) the joint distribution of brands

Question 18

Consider the following to answer the question(s) below:
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.

Identify the variables and tell whether each is categorical or quantitative.

Question 19

Prepare an appropriate chart to display the marginal distribution of age.

Question 20

Consider the following to answer the question(s) below:
A large national retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender.

Of the consumers who are female, the percentage who prefer Canon is

A) 63.74% (58/91)
B) 16.67% (58/348)
C) 9.31% (58/623)
D) 14.61% (91/623)
E) 55.86% (348/623)

Question 21

Consider the following to answer the question(s) below:
The option to buy extended warranties is commonplace with most electronics purchases. Does the type of purchase affect a consumer's willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table.
Of those who bought a digital camera, the percentage who purchased the warranty is

A) 41.67% (30/72)
B) 17.14% (72/420)
C) 7.14% (30/420)
D) 41.14% (72/175)
E) none of the above

Question 22

Consider the following to answer the question(s) below:
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 and shown in the table below.

Of the clients over age 50, the percentage who invest in mutual funds is

A) 53.1% (34/64)
B) 33.3% (34/102)
C) 18.1% (34/188)
D) 34.0% (64/188)
E) 54.3% (102/188)

Question 23

Consider the following to answer the question(s) below:
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 and shown in the table below.

The percentage of clients over age 50 is

A) 53.1% (34/64)
B) 33.3% (34/102)
C) 18.1% (34/188)
D) 34.0% (64/188)
E) 54.3% (102/188)

Question 24

Which of the following is a reason for constructing a joint frequency distribution?

A) to help analyze the relationship between the two variables
B) to determine the trend between the two variables
C) to measure the spread between two variables
D) to show the average of the two variables
E) to show the average and the spread of the two variables

Question 25

Consider the following to answer the question(s) below:
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 and shown in the table below.

Of the clients who invest in mutual funds, the percentage over age 50 is

A) 53.1% (34/64)
B) 33.3% (34/102)
C) 18.1% (34/188)
D) 34.0% (64/188)
E) 54.3% (102/188)

Question 26

Consider the following to answer the question(s) below:
The option to buy extended warranties is commonplace with most electronics purchases. Does the type of purchase affect a consumer's willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table.
Of those who made a purchase, the percentage who chose the warranty is

A) 41.67% (175/420)
B) 7.14% (30/420)
C) 17.14% (30/175)
D) 82.86% (145/175)
E) 71.43% (175/245)

Question 27

The city council has just voted to pass the budget for next year. If you were writing a report describing the budget so the citizens could understand how the total tax dollars will be spent, which of the following graphs might be most appropriate?

A) pie chart
B) scatter diagram
C) bar chart
D) histogram
E) A or C

Question 28

Consider the following to answer the question(s) below:
The option to buy extended warranties is commonplace with most electronics purchases. Does the type of purchase affect a consumer's willingness to pay extra for an extended warranty? Data for 420 consumers who purchased digital cameras and laptop computers from a leading electronics retailer are summarized in the table.
A bar chart or a pie chart can be used to display what type of data?

A) categorical
B) quantitative
C) continuous
D) cross-sectional
E) time series

Question 29

One characteristic of a bar chart is

A) The bars can be displayed either vertically or horizontally.
B) There can be no gaps between the bars.
C) The bars should be of different widths.
D) It is used to display the distribution of a continuous variable.
E) It shows cumulative frequency.

Question 30

A contingency table is used to display

A) the count for each possible joint occurrence of two variables
B) the cumulative frequency of two variables
C) the cumulative distribution of a variable with two possible outcomes
D) the relative frequency of one variable
E) none of the above

Question 31

A study was recently done in which the brand preference for coffee was analyzed against the gender of the shopper. The study consisted of 200 male shoppers and 300 female shoppers. Three different coffee brands were considered: A, B, and C. A total of 250 female shoppers preferred brand A and 25 female shoppers preferred brand C. The number of female shoppers that preferred brand B was:

A) 25
B) 100
C) 75
D) 50
E) 125

Question 32

The pie chart below for these data shows

A) the marginal distribution of client age
B) the conditional distribution of client age
C) the conditional distribution of investment type
D) the marginal distribution of investment type
E) the joint distribution of client age and investment type