AP Statistics 2.2: Comparing Categorical Summaries
Compare categorical distributions by using relative frequencies from two-way tables and explaining what the differences mean in context.
- Syllabus
- Effective Fall 2025
- Course
- AP Statistics
Compare categorical distributions by using relative frequencies from two-way tables and explaining what the differences mean in context.
To compare success rates for treating allergies at two clinics that specialize in treating allergy sufferers, researchers selected random samples of patient records from the two clinics. The following table summarizes the data.

Based on the relative frequency table in part (a-i), which clinic is more successful in treating allergy sufferers? Justify your answer.
Clinic A appears to be more successful in treating allergy sufferers than Clinic B. Clinic A was successful for 63.3% of the allergy sufferers it treated, while Clinic B was successful for only 51.5\% of the allergy sufferers it treated.
Additional Notes:
- Responses may be given as proportions or percentages.
- To satisfy component 1, numerical values for relative frequencies must be accurately reported to at least two decimal places, e.g., 0.36 or 0.37, 0.48 or 0.49, 0.63 or 0.64, 0.51 or 0.52.
- If a response in part (a-i) reports the relative proportions of the total (dividing the count in each of the four cells by 207) instead of the conditional relative frequencies, then component 2 may be satisfied in either of the following ways:
Concluding that Clinic A is more successful in treating allergies based on the larger proportion of successful cases (0.43 vs. 0.17)
Concluding that Clinic B is more successful in treating allergies based on the smaller proportion of unsuccessful cases (0.16 vs. 0.25).
- If a response reports incorrect values in part (a-i), then the justification in component 2 may use either the relative frequencies reported in the table in part (a-i) OR the correct conditional relative frequencies given in the model solution.
- To satisfy component 2, the response must make it clear that Clinic A is being compared to Clinic B, either by explicitly mentioning both clinics OR by reporting both relative frequencies that are being compared.
Model Solution
Scoring