Two-Way Table
In short: A two-way table is a grid that counts how many people or objects fall into each combination of two categorical variables, with totals along the edges.
8th GradeStatistics8.SP.A.4
What is Two-Way Table?
A two-way table sorts one group of people by two questions at once. One variable labels the rows, such as walks to school or not, and the other labels the columns, such as grade level. Each inside cell counts the people who match that row and that column.
The totals on the right and at the bottom are the marginal totals, and the corner holds the grand total. Every row total and every column total must add up to that same corner number, which makes missing cells easy to recover.
How to spot it
- A survey asks every person two yes-or-no or multiple-choice questions.
- A table shows counts with rows and columns and a total row at the bottom.
- Some cells are blank and the question asks you to fill them from the totals.
- You are asked what fraction or percent of one group also belongs to another category.
The method
- Identify the two variables and place one on the rows and the other on the columns.
- Enter each count in its cell, then add across for row totals and down for column totals.
- Use the rule that row totals and column totals both sum to the grand total to find any missing number.
- Divide the cell of interest by the right total to turn counts into fractions or percents.
Two-Way Table: solved example
Problem
A cafeteria survey of 90 students found that 52 prefer pizza and 38 prefer tacos. Among the 48 girls surveyed, 17 prefer tacos. How many boys prefer pizza?
Solution
Girls who prefer pizza: \(48 – 17 = 31\). Then boys who prefer pizza: \(52 – 31 = 21\).
Check with tacos: boys who prefer tacos are \(38 – 17 = 21\), so there are \(21 + 21 = 42\) boys, and \(48 + 42 = 90\). 21 boys prefer pizza.
Try it
Question 1
The row totals of a table are 45 and 55. What must the column totals add up to?
Show the answer
The grand total, \(45 + 55 = 100\).
Question 2
12 of 20 sixth graders and 9 of 30 seventh graders joined chess club. How many of the 50 students did not join?
Show the answer
Joined: \(12 + 9 = 21\). Not joined: \(50 – 21 = 29\).
Two-Way Table vs. Frequency Table
A frequency table tallies one variable in a single list. A two-way table tallies two variables at once, so you can compare groups, for example whether seventh and eighth graders walk at different rates. It adds a second direction, and with it the totals along both edges.
Keep going
Lessons
Worksheets and quizzes
Related words
- Relative Frequency
- Frequency Table
- Categorical and Quantitative Variables
- Conditional Probability
- Scatter Plot
- Percent
Whole dictionary: A–Z · 8th Grade · Statistics