AP Statatistics 1.2-1.10

The following table shows data for the 8 longest roller coasters in the world as of 2015.

Length (feet)	Type	Speed (miles per hour)	Height (feet)	Drop (feet)	Continent
8,133	Steel	95	318	310	Asia
7,442	Steel	50	107	102	Europe
7,359	Wood	65	110	135	North America
6,709	Steel	81	259	230	Asia
6,602	Steel	95	325	320	North America
6,595	Steel	93	310	300	North America
6,562	Steel	149	171	168	Asia
6,442	Wood	67	163	154	North America

Which of the following variables is categorical?

Responses

A

Length

B

Type

C

Speed

D

Height

E

Drop

Answer B

Correct. The variable assumes categorical values, i.e. , names, and not quantitative values.

Which of the following questions about cars in a school parking lot will allow for the collection of a set of categorical data?

Responses

A

How many blue cars are in the lot?

B

What are the gas mileages, in miles per gallon, of the cars in the lot?

C

What are the weights, in pounds, of the cars in the lot?

D

What is the number of cars in the lot with out-of-state license plates?

E

What are the colors of the cars in the lot?

Answer E

Correct. To answer this question, a set of data will be collected that consists of names for colors, which is a set of categorical data.

Data were collected on 100 United States coins minted in 2018. Which of the following represents a quantitative variable for the data collected?

Responses

A

The type of metal used in the coin

B

The value of the coin

C

The color of the coin

D

The person depicted on the face of the coin

E

The location where the coin was minted

Answer B

Correct. The value of a coin can be measured as a number.

The following frequency table shows the responses from a group of college students who were asked to choose their favorite flavor of ice cream.

Flavor	Frequency
Vanilla	100
Chocolate	65
Strawberry	35
Mint chip	45
Coffee	30
Butter pecan	25

Which of the following statements is not supported by the table?

Responses

A

The number of student responses is 300.

B

One-third of the students chose vanilla.

C

One-third of the students chose chocolate or strawberry.

D

One-fourth of the students chose mint chip or coffee.

E

One-half of the students chose vanilla or chocolate.

Answer E

Correct. The total frequency of students is 100+65+35+45+30+25=300. One-half of the students is 1/2(300) = 150. The number of students who chose vanilla or chocolate is 100+65. Since 165 ≠ 150, the statement “One-half of the students chose vanilla or chocolate” is not supported by the table.

The following relative frequency table shows the political party affiliation for a sample of 500 people in a certain town.

Political Party	Relative Frequency
Democrat	0.35
Republican	0.30
Independent	0.20
Green Party	0.11
Libertarian	0.03
Other	0.01

Which of the following statements is supported by the table?

Responses

A

The number of people affiliated with the Republicans is 30.

B

The number of people affiliated with the Independents is 100.

C

Less than half of the people are affiliated with the Democrats or the Republicans.

D

At least 200 people are affiliated with the Democrats.

E

At least 80 people are affiliated with the Green Party or the Libertarians.

Answer B

Correct. 20% of 500 is 100.

The following table summarizes the number of pies sold at a booth one day at a local farmers market.

Type of Pie	Frequency
Apple	18
Blueberry	14
Cherry	16
Key Lime	12
Peach	12
Pumpkin	18

Which of the following statements is supported by the table?

Responses

A

More cherry pies were sold than any other type of pie.

B

Twice as many apple pies as key lime pies were sold.

C

More than half the pies sold were apple.

D

Fewer than 50 pies were sold at the booth that day.

E

The combined percentage of key lime pies sold and pumpkin pies sold was less than 50%.

Answer E

Correct. The number of key lime pies sold is 12 and the number of pumpkin pies sold is 18. The combined total is 30, which is equal to approximately 33% of the pies sold. Therefore, the combined percentage is less than 50%.

A market researcher asked a group of men and women to choose their favorite color design from a sample of advertisements. The results are shown in the following table.

	Red with Black	Green with Black	Yellow with Black	Red with Blue	Green with Blue	Yellow with Blue
Men	21	15	8	12	35	9
Women	15	3	11	31	24	16

Which of the following statements is not supported by the table?

Responses

A

More men than women chose the color design red with black.

B

More women than men chose the color design yellow with black.

C

For men, the number who chose a design with black was greater than the number who chose a design with blue.

D

The color design chosen by the most people was green with blue.

E

The total number of men surveyed by the market researcher was equal to the total number of women surveyed by the market researcher.

Answer C

Correct. The statement is not supported. The number who chose a design with black was 44, but 56 chose a design with blue.

In a certain school district, students from grade 6 through grade 12 can participate in a school-sponsored community service activity. The following bar chart shows the relative frequencies of students from each grade who participate in the community service activity.

Which of the following statements is supported by the bar chart?

Responses

A

The greatest number of participating students was in grade 9.

B

The number of participating students in grade 6 was equal to the number of participating students in grade 7.

C

The relative frequency of all participating students in grades 6 and 7 combined was 0.60.

D

Grade 12 had the least relative frequency of participating students.

E

Grade 11 had the greatest relative frequency of participating students.

Answer D

Correct. The least relative frequency on the bar chart is 0.10, which corresponds to grade 12.

A child psychologist asked 100 five year olds and 50 ten year olds to name their favorite color. Their results are shown in the following table.

	Red	Orange	Yellow	Green	Blue	Purple
Five year olds	21	15	8	10	35	11
Ten year olds	7	2	6	15	12	8

Which of the following statements is supported by the table?

Responses

A

The percentage of five year olds who selected red or blue as their favorite color is greater than the percentage of ten year olds who selected red or blue as their favorite color.

B

The percentage of five year olds who selected yellow as their favorite color is greater than the percentage of ten year olds who selected yellow as their favorite color.

C

The percentage of children who selected red, yellow, or blue as their favorite color was equal for both ages.

D

Less than half of the five year olds selected red, yellow, or blue as their favorite color.

E

Less than half of the ten year olds selected red, yellow, or blue as their favorite color.

Answer A

Correct. The statement is supported by the table. The percentage of five year olds who selected red or blue as their favorite color is (25+35)/100 = 56%, while the percentage of ten year olds who selected red or blue as their favorite color is (7+12)/100 = 38% .

The following pie chart summarizes the results of a survey given to airlines about the primary reason for flight delays.

Which of the following statements is supported by the pie chart?

Responses

A

The reason given most frequently was runway closure.

B

More delays were caused by weather than by all other reasons combined.

C

More delays were caused by runway closure than were caused by overbooking.

D

Overbooking and runway closure accounted for greater than one-fourth of the reasons given for flight delays.

E

The combined percentage for other and runway closure was equal to the percentage for overbooking.

Answer B

Correct. The percentage for weather is greater than 50%.

A sample of 100 students from Liberty High School and a sample of 60 students from Central High School were asked what they planned to do after graduation. Responses fell into five categories: four-year university (4Y), community college (CC), join the workforce (W), join the military (M), or undecided (UD). The results are shown in the following bar chart.

Which of the following statements is supported by the bar chart?

Responses

A

For the category four-year university, the number of students from Central High School was 10 greater than the number of students from Liberty High School.

B

At Liberty High School, more students selected a four-year university than any other activity.

C

For the category join the workforce, the number of students from each school was equal.

D

At Central High School, the same number of students selected four-year university and military.

E

For the category undecided, the number of students from Liberty High School was 4 greater than the number of students from Central High School.

Answer E

Correct. Both bars reach to the 0.10 line, indicating 10% of the students. For Liberty High School, 10% of 100 is 10 students and for Central High School, 10% of 60 is 6 students. So for the category undecided, Liberty High School has 4 more students than Central High School.