AP Statistics Practice Quiz: Statistics for Two Categorical Variables

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

In a two-way table, how is a marginal relative frequency calculated?

A)A cell count divided by its row total.B)A row or column total divided by the grand total.C)A cell count divided by the grand total.D)A row total divided by a column total.

All Questions (14)

In a two-way table, how is a marginal relative frequency calculated?

A) A cell count divided by its row total.

B) A row or column total divided by the grand total.

C) A cell count divided by the grand total.

D) A row total divided by a column total.

Correct Answer: B

This directly matches the provided definition: 'Marginal relative frequencies are row or column totals divided by the grand total in a two-way table.'

Which of the following best describes a conditional relative frequency?

A) A frequency that represents the entire dataset, irrespective of any categories.

B) The total count in a row or column divided by the grand total.

C) A relative frequency calculated for a specific subgroup or condition within a contingency table.

D) The overall total number of observations in a study.

Correct Answer: C

This aligns with the definition 'A conditional relative frequency is a relative frequency for a specific part of a contingency table,' where 'specific part' implies a subgroup or condition.

According to the provided information, what are the two primary purposes of using summary statistics for two categorical variables?

A) To calculate the mean and standard deviation.

B) To create a scatterplot and find the correlation coefficient.

C) To compare distributions or determine association.

D) To find the grand total and individual cell counts.

Correct Answer: C

The content explicitly states, 'Summary statistics for two categorical variables can compare distributions or determine association.' The other options relate to quantitative data (A, B) or are basic components of a table, not the primary purpose of the summary statistics (D).

A researcher creates a two-way table to analyze the relationship between grade level (9th, 10th, 11th, 12th) and preferred lunch option (Pizza, Salad, Sandwich). If the researcher calculates the proportion of ALL students who prefer Pizza, what type of frequency is this?

A) A conditional relative frequency.

B) A marginal relative frequency.

C) A joint absolute frequency.

D) A categorical mean.

Correct Answer: B

This calculation involves the column total for 'Pizza' divided by the grand total of all students. This fits the definition of a marginal relative frequency ('row or column totals divided by the grand total'). It is not conditional because it is not restricted to a specific grade level.

Using the same scenario of grade level and lunch preference, a researcher wants to know the proportion of 10th graders who prefer Salad. The calculation for this value would be an example of what?

A) A marginal relative frequency.

B) A conditional relative frequency.

C) The grand total.

D) An association statistic.

Correct Answer: B

The calculation is restricted to a 'specific part' of the table—only the 10th graders. This is the essence of a conditional relative frequency. The denominator would be the total number of 10th graders, not the grand total.

When we calculate and compare statistics for two categorical variables, what are we fundamentally trying to understand?

A) The average value for each variable.

B) The potential relationship or association between the variables.

C) The spread of the data around a central point.

D) The total number of observations in the dataset.

Correct Answer: B

The content states that a key purpose is to 'determine association' between the two categorical variables. The other options are not relevant to categorical data analysis (A, C) or are too simplistic (D).

In a two-way table summarizing data on pet ownership (Dog, Cat, Neither) and housing type (House, Apartment), the number in the 'Total' column for the 'Dog' row divided by the grand total represents:

A) The conditional relative frequency of owning a dog, given that a person lives in a house.

B) The marginal relative frequency of owning a dog.

C) The conditional relative frequency of living in a house, given that a person owns a dog.

D) The joint relative frequency of owning a dog and living in a house.

Correct Answer: B

The calculation described is a row total ('Total' for the 'Dog' row) divided by the grand total. This is the precise definition of a marginal relative frequency provided in the content.

If a statistician compares the conditional relative frequencies of passing a driving test for students who took a prep course versus those who did not, what is the primary goal of this comparison?

A) To calculate the marginal frequency of passing the test.

B) To determine if there is an association between taking the prep course and passing the test.

C) To find the total number of students who took the test.

D) To calculate the overall pass rate for all students combined.

Correct Answer: B

By comparing the pass rates for two different groups (conditions), the statistician is looking to 'compare distributions' to 'determine association.' A significant difference between these conditional frequencies would suggest an association between the two variables. Option D describes a marginal frequency.

To find a marginal relative frequency for a specific category in a two-way table, you first need to find the total for that category's row or column and then divide by what?

A) The number of cells in the table.

B) The corresponding column or row total.

C) The grand total of all observations.

D) The count in the largest cell.

Correct Answer: C

The definition explicitly states that marginal relative frequencies are 'row or column totals divided by the grand total.'

A marketing team wants to know if there is a difference in social media platform preference (Platform X, Platform Y, Platform Z) between two age groups (Under 30, 30 and Over). Which of the following would be most useful for this analysis?

A) Calculating only the marginal relative frequencies for each platform.

B) Comparing the conditional relative frequencies of platform preference for each age group.

C) Finding the single largest cell count in the two-way table.

D) Calculating the grand total of all survey respondents.

Correct Answer: B

To see if there is a difference between the age groups, one must compare the distributions of platform preference within each age group. This requires calculating and comparing conditional relative frequencies, which directly addresses the goal of comparing distributions to find an association.

A survey asks about employment status (Employed, Unemployed) and level of education (High School, College, Graduate School). The value calculated by dividing the number of unemployed people with a college degree by the total number of people with a college degree is a(n):

A) Marginal relative frequency of unemployment.

B) Marginal relative frequency of having a college degree.

C) Conditional relative frequency of being unemployed, given a college degree.

D) Conditional relative frequency of having a college degree, given unemployment.

Correct Answer: C

The calculation is for a 'specific part' of the data: only those with a college degree. The result is the proportion of that specific group that is unemployed. This is the definition of a conditional relative frequency, with the condition being 'having a college degree.'

A contingency table, also known as a two-way table, is primarily used to display and analyze the relationship between what type of variables?

A) Two quantitative variables.

B) One quantitative and one categorical variable.

C) Two categorical variables.

D) A single categorical variable.

Correct Answer: C

The provided content is titled 'Statistics for Two Categorical Variables' and discusses two-way/contingency tables. This indicates these tables are the primary tool for organizing and analyzing data from two categorical variables.

If the conditional relative frequency of preferring Brand A coffee is nearly identical for both morning and evening coffee drinkers, what can be concluded?

A) There is a strong association between time of day and coffee preference.

B) There is likely little to no association between time of day and coffee preference.

C) The marginal frequency of preferring Brand A is very high.

D) Most people drink coffee in the morning.

Correct Answer: B

The purpose of comparing these statistics is to determine association. If the distributions are the same or very similar across different conditions (morning vs. evening), it suggests the variables are independent and there is no association between them.

What two numbers are needed to calculate a single marginal relative frequency from a two-way table?

A) A single cell count and its row total.

B) Two different cell counts.

C) A row or column total and the grand total.

D) A row total and a column total.

Correct Answer: C

This is a direct application of the definition: 'Marginal relative frequencies are row or column totals divided by the grand total.' Therefore, you need one of those totals and the grand total.