Two-Way Tables Statistics Example 2

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Example 2

medium
From 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.

Solution

  1. 1
    Step 1: Total who studied: 40+5=4540 + 5 = 45. Total who didn't study: 10+25=3510 + 25 = 35.
  2. 2
    Step 2: Percentage who passed among studiers: 4045×100≈88.9%\frac{40}{45} \times 100 \approx 88.9\%.
  3. 3
    Step 3: Percentage who passed among non-studiers: 1035×100≈28.6%\frac{10}{35} \times 100 \approx 28.6\%.

Answer

About 88.9% of students who studied passed, compared to about 28.6% of students who didn't study.
Two-way tables allow us to compute conditional percentages — the percentage of one outcome given a specific condition. Comparing conditional percentages across groups reveals potential associations between the two categorical variables.

About Two-Way Tables

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.

Learn more about Two-Way Tables →

More Two-Way Tables Examples

Example 1 easy

A survey of 60 students recorded their gender and whether they prefer cats or dogs. Boys who prefer

Example 3 medium

A two-way table shows transport to school: Walk (Year 7: 30, Year 8: 20), Bus (Year 7: 15, Year 8: 2

Example 4 hard

A two-way table shows exercise frequency and health rating for 200 adults: Exercise regularly — Good

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