--- title: "Two-Way Tables" description: "Construct and read two-way tables that sort the same people by two categories at once (e.g., year group against preferred sport); use row and column totals and relative frequencies to judge whether th" canonical: https://lightmysky.com/learn/mathematics/two-way-tables-mt_oD1Rgg52n3 source: https://lightmysky.com/learn/mathematics/two-way-tables-mt_oD1Rgg52n3.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Two-Way Tables Construct and read two-way tables that sort the same people by two categories at once (e.g., year group against preferred sport); use row and column totals and relative frequencies to judge whether the two categories are associated Subject: Mathematics · Area: Data & Statistics · Ages 12 to 14 Page: https://lightmysky.com/learn/mathematics/two-way-tables-mt_oD1Rgg52n3 ## Ready when they can - Build a two-way table from raw data on two categories collected from the same people - Read off joint and total frequencies (e.g., how many students both walk to school and pack their lunch) - Compare row or column relative frequencies to say whether two things seem linked (e.g., do pet owners do more sport?) ## Lesson: Two-Way Tables You already know how to read a table. A two-way table does one more job: it sorts the same group of people by two questions at once, not just one. **Example.** Ms. Ito asked 50 students two questions: do you have a pet, and do you play a sport? She put the answers in a two-way table. Plays sport No sport Total Has a pet 18 6 24 No pet 10 16 26 Total 28 22 50 The box where a row meets a column is called a cell. The 'Has a pet' row meets the 'Plays sport' column at 18. That means 18 students both have a pet and play a sport. The 'Total' row and column tell you about just one question at a time. At the bottom of the 'Plays sport' column, 28 students play a sport in total, no matter whether they have a pet. In the right-hand 'Total' column, 24 students have a pet, no matter what sport they play. *(drawing: 75% of pet owners play a sport. Only about 38% of students without a pet do. The two groups look quite different.)* **Tip.** Row totals are not always equal (24 pet owners, 26 without). That is why you compare percentages, not raw counts, when you want to know if two categories are linked. **Recap.** A two-way table sorts the same people by two questions at once; compare relative frequencies, not raw counts, to see if the two are linked. ## Practice 16 questions on this page, each with its working shown. ## Needs first - [Statistical Questions](https://lightmysky.com/learn/mathematics/statistical-questions-mt_4Ax4JPXJWD) - [Reading tables](https://lightmysky.com/learn/mathematics/reading-tables-mt_Cqm8iy48UI) - [Fractions, Decimals & Percentages](https://lightmysky.com/learn/mathematics/fractions-decimals-and-percentages-mt_hlGKg5M7qJ) ## Opens up - [Sets & Venn Diagrams](https://lightmysky.com/learn/mathematics/sets-and-venn-diagrams-mt_1YwOCMMwD8) - [Conditional Probability from Tables and Venn Diagrams](https://lightmysky.com/learn/mathematics/conditional-probability-from-tables-and-venn-diagrams-mt_Vx88ugViYP)