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2.3 Statistics for Two Categorical Variables

Part of Exploring Two-Variable Data in AP® Statistics. Read the opening section, then create a free account for the full interactive lesson, practice, and progress tracking.

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Relative Frequencies in Two-Way Tables

From a two-way table, we can compute several types of relative frequencies:

Joint relative frequency:
cell countgrand total\frac{\text{cell count}}{\text{grand total}}
→ proportion of all individuals that fall in that specific cell
Marginal relative frequency:
row or column totalgrand total\frac{\text{row or column total}}{\text{grand total}}
→ proportion of all individuals in that row/column category
Conditional relative frequency:
cell countrow or column total\frac{\text{cell count}}{\text{row or column total}}
→ proportion within a specific row or column (condition)

Example: 200 students surveyed by grade and favorite subject:

  • Joint: (juniors who prefer math)/200{(\text{juniors who prefer math})/200}
  • Marginal: (all juniors)/200{(\text{all juniors})/200}
  • Conditional: (juniors who prefer math)/(all juniors){(\text{juniors who prefer math})/(\text{all juniors})}

In this unit

9 lessons

  1. 2.1Introducing Statistics: Are Variables Related?Preview lesson
  2. 2.2Representing Two Categorical VariablesPreview lesson
  3. 2.3Statistics for Two Categorical VariablesThis lesson
  4. 2.4Representing the Relationship Between Two Quantitative VariablesPreview lesson
  5. 2.5CorrelationPreview lesson
  6. 2.6Linear Regression ModelsPreview lesson
  7. 2.7ResidualsPreview lesson
  8. 2.8Least Squares RegressionPreview lesson
  9. 2.9Analyzing Departures from LinearityPreview lesson

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