Question

Suppose a certain magazine evaluates products for consumers. The following table contains data for 15 compact sports utility vehicles (SUVs) from a certain year.

• Vehicle—name of vehicle
• Overall score—awarded based on a variety of measures, including those in this data set
• Recommended—Consumer Reports recommends the vehicle or not
• Owner satisfaction—satisfaction on a five-point scale based on the percentage of owners who would purchase the vehicle again (−−, −, 0, +, ++)
• Overall miles per gallon–miles per gallon achieved in a 150-mile test trip
• Acceleration (0–60 sec)—time in seconds it takes vehicle to reach 60 miles per hour from a standstill with the engine idling

Vehicle	Overall Score	Recommended	Owner Satisfaction	Overall Miles Per Gallon	Acceleration (0–60) Sec
SUV 1	82	Yes	+	25	8.9
SUV 2	81	Yes	++	26	8.8
SUV 3	79	Yes	++	23	9.5
SUV 4	71	Yes	++	23	9.7
SUV 5	69	Yes	++	23	8.8
SUV 6	69	Yes	+	22	9.8
SUV 7	67	Yes	0	22	10.3
SUV 8	65	No	−	20	8.7
SUV 9	63	No	+	24	10.5
SUV 10	61	No	0	23	10.2
SUV 11	61	No	0	30	10.3
SUV 12	55	No	0	25	8.6
SUV 13	55	No	0	21	7.4
SUV 14	53	No	−	21	10.9
SUV 15	48	No	0	23	10

(a) How many variables are in the data set?

(b) Which of the variables are categorical? (Select all that apply.)

Overall Score

Recommended

Owner Satisfaction

Overall Miles Per Gallon

Acceleration (0–60) Sec

Which of the variables are quantitative? (Select all that apply.)

Overall Score

Recommended

Owner Satisfaction

Overall Miles Per Gallon

Acceleration (0–60) Sec

(c) What percentage of these 15 vehicles are recommended? (Round your answer to the nearest percent.)

%

(d) What is the average of the overall miles per gallon across all 15 vehicles? (Round your answer to one decimal place.)

miles per gallon

(e) For owner satisfaction, construct a bar chart showing the percentage frequency for each of the owner satisfaction ratings.

A.

A graph has a horizontal axis labeled "Owner Satisfaction" and a vertical axis labeled "Percent Frequency" with values from 0 to 50. The bar graph has 5 bars. Each bar is associated with a label and an approximate value as listed below.

• −−: 0
• −: 13.3
• 0: 40
• +: 20
• ++: 26.7

B.

A graph has a horizontal axis labeled "Owner Satisfaction" and a vertical axis labeled "Percent Frequency" with values from 0 to 50. The bar graph has 5 bars. Each bar is associated with a label and an approximate value as listed below.

• −−: 0
• −: 13.3
• 0: 20
• +: 26.7
• ++: 40

C.

A graph has a horizontal axis labeled "Owner Satisfaction" and a vertical axis labeled "Percent Frequency" with values from 0 to 50. The bar graph has 5 bars. Each bar is associated with a label and an approximate value as listed below.

• −−: 0
• −: 13.3
• 0: 20
• +: 40
• ++: 26.7

D.

A graph has a horizontal axis labeled "Owner Satisfaction" and a vertical axis labeled "Percent Frequency" with values from 0 to 50. The bar graph has 5 bars. Each bar is associated with a label and an approximate value as listed below.

• −−: 0
• −: 26.7
• 0: 40
• +: 20
• ++: 13.3

(f) Show the frequency distribution for acceleration using the following intervals: 7.0–7.9, 8.0–8.9, 9.0–9.9, and 10.0–10.9. Construct a histogram showing the frequencies of each interval.

A.

A graph has a horizontal axis labeled "Acceleration (0-60) Sec" and a vertical axis labeled "Frequency" with values from 1 to 7. The bar graph has 4 bars. Each bar is associated with a label and an approximate value as listed below.

• 7.0–7.9: 1
• 8.0–8.9: 5
• 9.0–9.9: 3
• 10.0–10.9: 6

B.

A graph has a horizontal axis labeled "Acceleration (0-60) Sec" and a vertical axis labeled "Frequency" with values from 1 to 7. The bar graph has 4 bars. Each bar is associated with a label and an approximate value as listed below.

• 7.0–7.9: 1
• 8.0–8.9: 3
• 9.0–9.9: 5
• 10.0–10.9: 6

C.

A graph has a horizontal axis labeled "Acceleration (0-60) Sec" and a vertical axis labeled "Frequency" with values from 1 to 7. The bar graph has 4 bars. Each bar is associated with a label and an approximate value as listed below.

• 7.0–7.9: 1
• 8.0–8.9: 5
• 9.0–9.9: 3
• 10.0–10.9: 4

D.

A graph has a horizontal axis labeled "Acceleration (0-60) Sec" and a vertical axis labeled "Frequency" with values from 1 to 7. The bar graph has 4 bars. Each bar is associated with a label and an approximate value as listed below.

• 7.0–7.9: 1
• 8.0–8.9: 3
• 9.0–9.9: 4
• 10.0–10.9: 5

Answer 1

(a) There are 5 variables in the data, they are

1.Overall score—awarded based on a variety of measures, including those in this data set

2. Recommended—Consumer Reports recommends the vehicle or not

3.Owner satisfaction—satisfaction on a five-point scale based on the percentage of owners who would purchase the vehicle again (−−, −, 0, +, ++)

4. Overall miles per gallon–miles per gallon achieved in a 150-mile test trip

5. Acceleration (0–60 sec)—time in seconds it takes vehicle to reach 60 miles per hour from a standstill with the engine idling

(b) The following are two categorical variables (without numbers), they are

1. Recommended—Consumer Reports recommends the vehicle or not(Yes or No)

2.Owner satisfaction—satisfaction on a five-point scale based on the percentage of owners who would purchase the vehicle again (−−, −, 0, +, ++)

The following are three quantitative variables(with numbers), they are

1.Overall score—awarded based on a variety of measures, including those in this data set

2. Overall miles per gallon–miles per gallon achieved in a 150-mile test trip

3. Acceleration (0–60 sec)—time in seconds it takes vehicle to reach 60 miles per hour from a standstill with the engine idling.

       (c)   The percentage of the 15 vehicles are recommended =

= (Number of ‘yes’/15)*100 = (7/15)*100=700/15 = 46.6% =47%

(d) The average of the overall miles per gallon across all 15 vehicles

=Sum of overall miles per gallon/15 =

= (25+26+…+23)/15 = 351/15 = 23.4 miles per gallon

(e) For owner satisfaction, a bar chart showing the percentage frequency for each of the owner satisfaction ratings is constructed as .follows:

Percentage frequency of a rating = (Number of particular rating/15)*100

Rating	% frequency of rating
minus minus	0
minus	13.3
zero	40
plus	20
plus plus	26.7

Ans. A.

A graph has a horizontal axis labeled "Owner Satisfaction" and a vertical axis labeled "Percent Frequency" with values from 0 to 50. The bar graph has 5 bars. Each bar is associated with a label and an approximate value as listed below.

· −−: 0

· −: 13.3

· 0: 40

· +: 20

· ++: 26.7

(f) The construction of histogram showingnthe frequency distribution for acceleration using the following intervals: 7.0–7.9, 8.0–8.9, 9.0–9.9, and 10.0–10.9 is as follows:

Accelaration	frequency of accelaration
7-7.9	1
8-8.9	5
9-9.9	3
10-10.9	6

Ans. A.

A graph has a horizontal axis labeled "Acceleration (0-60) Sec" and a vertical axis labeled "Frequency" with values from 1 to 7. The bar graph has 4 bars. Each bar is associated with a label and an approximate value as listed below.

· 7.0–7.9: 1

· 8.0–8.9: 5

· 9.0–9.9: 3

· 10.0–10.9: 6