PrepGo

AP Statistics Practice Quiz: Expected Counts in Two-Way Tables

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

Test your understanding with short quizzes. This quiz has 7 questions to check your progress.

Question 1 of 7

A survey of 150 people recorded their preferred type of music and their age group. The results are summarized in the table below. What is the expected count of Teens who prefer Rock?

All Questions (7)

A survey of 150 people recorded their preferred type of music and their age group. The results are summarized in the table below. What is the expected count of Teens who prefer Rock?

A) 37.33

B) 50.00

C) 26.67

D) 80.00

Correct Answer: A

The expected count is calculated as (row total * column total) / table total. The row total for 'Teens' is 80, the column total for 'Rock' is 70, and the table total is 150. Therefore, the expected count is (80 * 70) / 150 = 5600 / 150 ≈ 37.33.

A researcher is studying the relationship between housing type and pet ownership. Based on the data collected in the table below, what is the expected count of apartment dwellers who own a cat?

A) 30.00

B) 23.33

C) 46.67

D) 35.00

Correct Answer: B

First, calculate the necessary totals. The row total for 'Apartment' is 20 + 30 = 50. The column total for 'Cat' is 40 + 30 = 70. The table total is 60 + 40 + 20 + 30 = 150. The expected count is (row total * column total) / table total = (50 * 70) / 150 ≈ 23.33.

The table below summarizes the subscription plans chosen by new and existing customers. Which expression correctly sets up the calculation for the expected count of Existing Customers choosing Plan B?

A) (80 * 300) / 150

B) (150 * 150) / 300

C) (70 * 150) / 300

D) (80 * 150) / 300

Correct Answer: B

The formula for the expected count is (row total * column total) / table total. For the cell representing 'Existing Customer' and 'Plan B', the row total is 150, the column total is 150, and the table total is 300. Therefore, the correct expression is (150 * 150) / 300.

A survey of 200 high school students asked about their primary mode of transportation to school and their grade level. Of the students surveyed, 120 are underclassmen (9th/10th grade) and 80 are upperclassmen (11th/12th grade). Overall, 50 students walk to school. What is the expected number of underclassmen who walk to school?

A) 20

B) 30

C) 50

D) 60

Correct Answer: B

The expected count is found by multiplying the row total (120 underclassmen) by the column total (50 students who walk) and dividing by the table total (200 students). The calculation is (120 * 50) / 200 = 6000 / 200 = 30.

To calculate the expected count for a single cell in a two-way table, which three values are required?

A) The observed count in the cell, the row total, and the column total

B) The row total, the column total, and the table total

C) The observed count in the cell, the table total, and the row total

D) All of the row totals and all of the column totals

Correct Answer: B

The formula for the expected count in a cell is (row total * column total) / table total. Therefore, the three necessary components are the total for that cell's row, the total for that cell's column, and the overall table total.

In a two-way table summarizing data from 500 individuals, the expected count for a particular cell is 40. The total for the column containing this cell is 100. What is the total for the row containing this cell?

A) 80

B) 125

C) 200

D) 250

Correct Answer: C

Using the formula Expected Count = (Row Total * Column Total) / Table Total, we can solve for the unknown Row Total. Plugging in the given values: 40 = (Row Total * 100) / 500. Rearranging the equation gives Row Total = (40 * 500) / 100 = 20000 / 100 = 200.

The partially completed table below shows movie genre preferences for two groups. What is the expected count for a person in Group 2 who prefers Action?

A) 60.0

B) 50.0

C) 55.0

D) 45.0

Correct Answer: C

First, determine the row total for Group 2 by subtracting the Group 1 total from the table total: 200 - 90 = 110. Then, use the formula for expected count: (row total for Group 2 * column total for Action) / table total. This is (110 * 100) / 200 = 11000 / 200 = 55.0.