AP Statistics Practice Quiz: Representing a Categorical Variable with Tables

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 14 questions to check your progress.

Question 1 of 14

A statistics student surveys their classmates about their favorite type of movie. The student records the number of classmates who chose each genre. Which of the following should be used to display these counts?

A)A frequency tableB)A relative frequency tableC)A proportion tableD)A rate table

All Questions (14)

A) A frequency table

B) A relative frequency table

C) A proportion table

D) A rate table

Correct Answer: A

According to the provided content, a frequency table is used to show the counts for each category of a categorical variable.

A researcher wants to display the proportion of people in a sample who belong to different blood type groups (A, B, AB, O). Which type of table would be most appropriate for showing these proportions?

A) A frequency table

B) A relative frequency table

C) A counts table

D) A categorical table

Correct Answer: B

The content states that a relative frequency table is used to show proportions for each category.

A local animal shelter has 50 animals. The table below shows the frequency of different types of animals. What is the relative frequency of cats at the shelter? | Animal Type | Frequency | |-------------|-----------| | Dog | 22 | | Cat | 20 | | Other | 8 |

A) 20

B) 0.20

C) 0.40

D) 0.44

Correct Answer: C

Relative frequency is the proportion, calculated by dividing the count for a category by the total count. The frequency of cats is 20, and the total number of animals is 50. Therefore, the relative frequency is 20/50 = 0.40.

A survey of 200 high school students asked about their primary source of news. The results are shown in the relative frequency table below. How many students reported 'Social Media' as their primary source? | News Source | Relative Frequency | |------------------|--------------------| | Television | 0.15 | | Social Media | 0.60 | | News Websites | 0.20 | | Print | 0.05 |

A) 60

B) 100

C) 120

D) 150

Correct Answer: C

To find the count (frequency) from a relative frequency, multiply the relative frequency by the total number of individuals. In this case, 0.60 * 200 = 120 students.

If a relative frequency for a certain category is 0.25, what is the equivalent percentage?

A) 0.25%

B) 2.5%

C) 25%

D) 250%

Correct Answer: C

The provided content states that percentages and relative frequencies provide the same information. To convert a proportion (relative frequency) to a percentage, multiply by 100. So, 0.25 * 100 = 25%.

A manager at a coffee shop claims that 'Espresso' is the least popular drink. Which statement uses the data from the frequency table below to justify this claim? | Drink Type | Frequency | |------------|-----------| | Latte | 110 | | Cappuccino | 85 | | Espresso | 45 | | Drip Coffee| 90 |

A) The claim is justified because Espresso has a frequency of 45, which is the lowest count among all drink types.

B) The claim is not justified because Latte has the highest frequency of 110.

C) The claim is justified because the total number of drinks is 330.

D) The claim is not justified because the relative frequency of Espresso is approximately 0.136.

Correct Answer: A

The content specifies that counts can be used to justify claims. The claim is that Espresso is the least popular. The frequency table shows the count for Espresso (45) is lower than the counts for Latte (110), Cappuccino (85), and Drip Coffee (90), which supports the manager's claim.

What is the primary difference between a frequency table and a relative frequency table for a categorical variable?

A) A frequency table shows percentages, while a relative frequency table shows counts.

B) A frequency table shows counts, while a relative frequency table shows proportions.

C) A frequency table is used for quantitative data, while a relative frequency table is for categorical data.

D) There is no difference; the terms are interchangeable.

Correct Answer: B

As stated in the provided content, a frequency table shows the counts for each category, whereas a relative frequency table shows the proportions (or fractions) for each category.

The table below shows the distribution of grades in a history class. Which of the following is a correct description of the data in the table? | Grade | Frequency | |-------|-----------| | A | 8 | | B | 12 | | C | 6 | | D/F | 4 |

A) The proportion of students who earned an A is 8.

B) More than half the class earned a grade of B or higher.

C) The count of students who earned a C is 0.20.

D) The rate of students earning a D or F is the highest in the class.

Correct Answer: B

To describe the data, we first find the total number of students: 8 + 12 + 6 + 4 = 30. The number of students earning a B or higher (A or B) is 8 + 12 = 20. Since 20 is more than half of 30, this statement is a correct description of the data.

A city council member claims that public transportation is underutilized. A survey of 500 commuters produced the relative frequency table below. Which statement best uses a relative frequency from the table to support the council member's claim? | Commute Method | Relative Frequency | |------------------|--------------------| | Personal Car | 0.72 | | Public Transport | 0.12 | | Carpool | 0.10 | | Other | 0.06 |

A) The claim is supported because only 0.12, or 12%, of commuters use public transport, a small proportion of the total.

B) The claim is not supported because 60 people use public transport.

C) The claim is supported because the proportion of commuters using a personal car is 0.72.

D) The claim is not supported because the total relative frequency is 1.00.

Correct Answer: A

The claim is that public transport is underutilized. The relative frequency of 0.12 for Public Transport indicates that only 12% of the surveyed commuters use this method. This small proportion compared to other methods, especially Personal Car (72%), provides strong evidence to justify the claim.

A company has 250 employees. A frequency table shows that 75 employees are in the Sales department. In a relative frequency table for this data, what value would be shown for the Sales department?

A) 75

B) 0.30

C) 30

D) 0.75

Correct Answer: B

A relative frequency table shows proportions. To calculate the proportion for the Sales department, divide its frequency (count) by the total number of employees: 75 / 250 = 0.30.

Which of the following provides the same information as a proportion?

A) A raw count

B) A percentage

C) A total frequency

D) A category label

Correct Answer: B

The provided content explicitly states that percentages, relative frequencies, and rates provide the same information as proportions.

A survey of 150 students about their favorite academic subject is partially summarized in the frequency table below. What is the relative frequency of students whose favorite subject is Math? | Subject | Frequency | |-----------|-----------| | English | 35 | | Science | 40 | | History | 30 | | Math | ? |

A) 45

B) 0.25

C) 0.30

D) 0.33

Correct Answer: C

First, find the frequency for Math. The total is 150 students. The sum of the other subjects is 35 + 40 + 30 = 105. So, the frequency for Math is 150 - 105 = 45. Next, calculate the relative frequency for Math by dividing its frequency by the total: 45 / 150 = 0.30.

A frequency table is created for the categorical variable 'Eye Color' from a sample of 80 people. If the count for 'Blue' eyes is 20, which of the following statements correctly describes this finding?

A) The proportion of people with blue eyes is 20.

B) The rate of blue eyes is 0.20 per person.

C) The relative frequency of blue eyes is 0.25.

D) The frequency of non-blue eyes is 20.

Correct Answer: C

To describe the data using relative frequency, we calculate the proportion. The count for 'Blue' is 20 and the total sample size is 80. The relative frequency is the count divided by the total: 20 / 80 = 0.25.

A student claims that a new brand of fertilizer is effective. They grow 50 plants, and the frequency table shows the health of the plants after one month. Which statement provides the strongest justification for the student's claim based on the data? | Plant Health | Frequency | |--------------|-----------| | Excellent | 28 | | Good | 15 | | Poor | 7 |

A) The claim is justified because the frequency of 'Poor' plants is only 7.

B) The claim is justified because the combined relative frequency of 'Excellent' and 'Good' plants is 0.86.

C) The claim is not justified because the relative frequency of 'Excellent' plants is only 0.56.

D) The claim is not justified because 15 plants were only in 'Good' health.

Correct Answer: B

To justify the claim of effectiveness, we should look at the proportion of plants that are healthy. The count of 'Excellent' or 'Good' plants is 28 + 15 = 43. The relative frequency is 43 / 50 = 0.86. This high proportion (86%) of healthy plants provides a strong justification for the claim that the fertilizer is effective.