Two-Way Frequency Tables
A free Algebra I lesson from the “Statistics and Data Analysis” unit, with a worked example and practice problems including step-by-step solutions.
A two-way frequency table organizes counts by two categorical variables — rows for one variable, columns for the other. Inside cells are joint frequencies; row and column totals are marginal frequencies. Conditional frequencies divide a joint count by a row or column total to ask 'within this group, what percent...?' In Statistics and Data Analysis, students need more than a memorized rule: they need to recognize the structure, select a method, carry out the algebra cleanly, and interpret the answer in a graph, table, equation, or real context. The expanded practice now mixes skill fluency, transfer questions, and cumulative review so the lesson builds durable Algebra I readiness.
What you'll learn
- Read joint, marginal, and total frequencies from a two-way table
- Compute conditional frequencies (one group within another)
- Express frequencies as percentages of a chosen total
Worked example
Problem. 100 students were surveyed. 15 are in band and play sports; 10 are in band only; 35 play sports only; 40 do neither. How many play sports total?
- Plays sports = (band AND sports) + (sports only).
- = 15 + 35 = 50.
- Connect the result back to Two-Way Frequency Tables so the method and meaning are both clear.
- Check the result against the original representation before writing the final answer.
Answer: 50
Lesson preview: this page shows 5 practice items. The interactive activity contains 28 practice items and 15 quiz items (typed response and multiple choice). Counts include repeated prompts and variants.
Practice problems
1. Out of 100 students: 15 are in band and play sports, 10 in band only, 35 play sports only, 40 do neither. How many are in band?
Show solution
- Band = (band AND sports) + (band only) = 15 + 10 = 25.
Answer: 25
2. Same survey. How many play sports AND are in band?
Show solution
- The joint cell for both is 15.
Answer: 15
3. Same survey. Total students?
Show solution
- Sum of all four cells: 15 + 10 + 35 + 40 = 100.
Answer: 100
4. Same survey. What percent play sports?
Show solution
- 50 out of 100 = 50%.
Answer: 50
5. Same survey. What percent are in band?
Show solution
- 25 out of 100 = 25%.
Answer: 25
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