Practice Two-Way Tables in Statistics
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A two-way table (contingency table) displays the frequency of data categorized by two different categorical variables simultaneously, with one variable in rows and the other in columns, allowing comparison of distributions across groups.
A two-way table is like a spreadsheet that shows how two questions relate. 'Do you like pizza?' and 'Are you a kid or adult?' becomes a 2 \times 2 grid showing how many kid pizza-lovers, adult pizza-lovers, etc.
Example 1
easyA survey of 60 students recorded their gender and whether they prefer cats or dogs. Boys who prefer cats: 8, boys who prefer dogs: 17, girls who prefer cats: 15, girls who prefer dogs: 20. Organise this into a two-way table with row and column totals.
Example 2
mediumFrom the two-way table: Passed exam — studied (40), didn't study (10); Failed exam — studied (5), didn't study (25). Calculate the percentage of students who passed among those who studied, and among those who didn't study.
Example 3
mediumA two-way table shows transport to school: Walk (Year 7: 30, Year 8: 20), Bus (Year 7: 15, Year 8: 25), Car (Year 7: 5, Year 8: 10). What percentage of Year 8 students take the bus?
Example 4
hardA two-way table shows exercise frequency and health rating for 200 adults: Exercise regularly — Good health: 70, Fair: 20, Poor: 10. Don't exercise regularly — Good health: 30, Fair: 40, Poor: 30. Is there an association between exercise and health? Support your answer with conditional percentages.