1. **State the problem:** We have a two-way table showing favorite movie genres by gender with some missing values. We need to complete the table and then find relative frequencies for given descriptions. 2. **Complete the table:** - Total students = 500 - Male total = 260 - Female total = 500 - 260 = 240 - Action total = 116 - Comedy total = 121 - Science-fiction total = unknown - Drama total = unknown 3. **Fill missing male values:** - Male Action = 66 - Male Drama = 61 - Male Comedy + Male Sci-Fi = 260 - (66 + 61) = 260 - 127 = 133 4. **Fill missing female values:** - Female Drama = 70 - Female Sci-Fi = 58 - Female Comedy = 240 - (58 + 70) = 240 - 128 = 112 5. **Fill missing totals for genres:** - Comedy total = 121, so Male Comedy = 121 - Female Comedy = 121 - 112 = 9 - Science-fiction total = Male Sci-Fi + Female Sci-Fi = ? - Male Sci-Fi = 133 - Male Comedy = 133 - 9 = 124 - Science-fiction total = 124 + 58 = 182 - Drama total = Male Drama + Female Drama = 61 + 70 = 131 6. **Verify totals:** - Action total = 116 (given) - Comedy total = 121 (given) - Science-fiction total = 182 (calculated) - Drama total = 131 (calculated) - Sum of genre totals = 116 + 121 + 182 + 131 = 550 (which is more than 500, so re-check calculations) 7. **Re-check calculations:** - Total students = 500 - Sum of genre totals must be 500 - Given totals: Action = 116, Comedy = 121, so sum of Sci-Fi and Drama = 500 - (116 + 121) = 500 - 237 = 263 - Drama total = 131 (from step 5) - So Sci-Fi total = 263 - 131 = 132 8. **Adjust male Sci-Fi:** - Male Sci-Fi + Female Sci-Fi = 132 - Female Sci-Fi = 58 (given) - Male Sci-Fi = 132 - 58 = 74 9. **Adjust male Comedy:** - Male Comedy + Male Sci-Fi = 133 (from step 3) - Male Sci-Fi = 74 - Male Comedy = 133 - 74 = 59 10. **Final completed table:** | | Action | Comedy | Sci-Fi | Drama | Total | |----------|--------|--------|--------|-------|-------| | Male | 66 | 59 | 74 | 61 | 260 | | Female | 50 | 62 | 58 | 70 | 240 | | Total | 116 | 121 | 132 | 131 | 500 | (Note: Female Action = 116 - 66 = 50, Female Comedy = 121 - 59 = 62) 11. **Calculate relative frequencies:** - Relative frequency = (count / total) * 100% 7. Relative frequency of people whose favorite genre is action: $$\frac{116}{500} \times 100 = 23.2\% \approx 23\%$$ 8. Relative frequency of female students: $$\frac{240}{500} \times 100 = 48\%$$ 9. Of male students, relative frequency of those whose favorite genre is science fiction: $$\frac{74}{260} \times 100 \approx 28.46\% \approx 28\%$$ 10. Relative frequency of students whose favorite genre is drama: $$\frac{131}{500} \times 100 = 26.2\% \approx 26\%$$ 11. Of students whose favorite genre is comedy, relative frequency of female students: $$\frac{62}{121} \times 100 \approx 51.24\% \approx 51\%$$ 12. **Match with given percentages:** - 7: 23% (E) - 8: 48% (B) - 9: 28% (F) - 10: 26% (D) - 11: 51% (C)