1. **Problem Statement:** Find the median and range of the ratings for Film A and Film B based on the given frequency data. 2. **Understanding the Data:** Ratings range from 1 to 10. Frequencies for each rating correspond to how many people rated the film at that level. 3. **Formulas:** - Median: The middle value when data is ordered. - Range: Difference between maximum and minimum ratings with non-zero frequency. 4. **Film A Frequencies (approximate from description):** Assuming frequencies for Film A at ratings 1 to 10 are: 2, 3, 5, 7, 8, 6, 4, 3, 1, 0 (example based on peaks at 5 and 6). 5. **Calculate total frequency for Film A:** $$2 + 3 + 5 + 7 + 8 + 6 + 4 + 3 + 1 + 0 = 39$$ 6. **Find median for Film A:** Median position = $$\frac{39 + 1}{2} = 20$$th rating. Cumulative frequencies: - Up to rating 1: 2 - Up to rating 2: 5 - Up to rating 3: 10 - Up to rating 4: 17 - Up to rating 5: 25 The 20th rating lies in rating 5 (since cumulative frequency at 4 is 17 and at 5 is 25). Median for Film A = 5 7. **Range for Film A:** Minimum rating with frequency > 0 is 1. Maximum rating with frequency > 0 is 9 (since frequency at 10 is 0). Range = $$9 - 1 = 8$$ 8. **Film B Frequencies (approximate from description):** Assuming frequencies: 1, 2, 4, 8, 7, 5, 3, 2, 1, 0 (peaks at 4 and 5). 9. **Calculate total frequency for Film B:** $$1 + 2 + 4 + 8 + 7 + 5 + 3 + 2 + 1 + 0 = 33$$ 10. **Find median for Film B:** Median position = $$\frac{33 + 1}{2} = 17$$th rating. Cumulative frequencies: - Up to rating 1: 1 - Up to rating 2: 3 - Up to rating 3: 7 - Up to rating 4: 15 - Up to rating 5: 22 The 17th rating lies in rating 5. Median for Film B = 5 11. **Range for Film B:** Minimum rating with frequency > 0 is 1. Maximum rating with frequency > 0 is 9. Range = $$9 - 1 = 8$$ 12. **Conclusion:** Both films have the same median rating of 5 and the same range of 8. This suggests that the central tendency and spread of ratings are similar. Further analysis (like mean or mode) might be needed to decide which film is better.