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 table that displays the frequency of data categorized by two different variables, allowing comparison 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.