1. **Problem statement:** Estimate the number of students whose obtained marks are between 35 and 40 from the given grouped data. 2. **Given data:** - Marks intervals: 30-40, 40-50, 50-60, 60-70, 70-80 - Number of students: 31, 42, 51, 35, 31 3. **Approach:** Since the data is grouped, we assume uniform distribution of students within each interval. 4. **Step 1:** Find the number of students per mark in the 30-40 interval. - Interval width = $40 - 30 = 10$ - Number of students in 30-40 = 31 - Students per mark = $\frac{31}{10} = 3.1$ 5. **Step 2:** Calculate students between 35 and 40. - Range width = $40 - 35 = 5$ - Estimated students = $3.1 \times 5 = 15.5$ 6. **Final answer:** Approximately **16** students obtained marks between 35 and 40.