1. **Problem statement:** We have two bar charts showing the number of books read by Year 13 students and the types of books read. We need to find: a) The median number of books read or state if it's impossible. b) The median type of book read or state if it's impossible. c) Whether it is possible to calculate the modal number of books read and the modal type of book read, with an explanation. 2. **Data from the bar charts:** - Number of books read and their frequencies: - 0 books: 0 students - 1 book: 15 students - 2 books: 10 students - 3 books: 25 students - 4 books: 30 students - Types of books read and their frequencies: - Poetry: 50 - Prose: 70 - Non-fiction: 70 - Other: 50 3. **Step a) Find the median number of books read:** - Total students = $0 + 15 + 10 + 25 + 30 = 80$ - Median position = $\frac{80 + 1}{2} = 40.5$th student when data is ordered. - Cumulative frequencies: - Up to 0 books: 0 - Up to 1 book: 15 - Up to 2 books: 15 + 10 = 25 - Up to 3 books: 25 + 25 = 50 - The 40.5th student lies between 26 and 50, so median number of books read is 3. 4. **Step b) Find the median type of book read:** - Total frequency = $50 + 70 + 70 + 50 = 240$ - Median position = $\frac{240 + 1}{2} = 120.5$th book type when data is ordered. - Cumulative frequencies: - Poetry: 50 - Prose: 50 + 70 = 120 - Non-fiction: 120 + 70 = 190 - The 120.5th book lies between 121 and 190, so median type is Non-fiction. 5. **Step c) Modal number and type of books read:** - Mode is the value with the highest frequency. - Number of books read frequencies: 0 (0), 1 (15), 2 (10), 3 (25), 4 (30) - Highest frequency is 30 for 4 books, so modal number of books read is 4. - Types of books read frequencies: Poetry (50), Prose (70), Non-fiction (70), Other (50) - Highest frequency is 70 for both Prose and Non-fiction. - Since there are two modes, the data is bimodal. - Therefore, it is possible to calculate the modal number of books read (4) and the modal type of book read (Prose and Non-fiction). **Final answers:** - Median number of books read: 3 - Median type of book read: Non-fiction - Modal number of books read: 4 - Modal type of book read: Prose and Non-fiction (bimodal)