1. **Problem statement:** We have a cumulative frequency diagram for 100 students recording the time $t$ (in minutes) taken to eat a pizza. We need to estimate: (i) the median time, (ii) the interquartile range (IQR), (iii) the number of students taking more than 11 minutes. 2. **Understanding cumulative frequency:** The cumulative frequency curve shows the total number of students who took up to a certain time to finish eating. - Median corresponds to the time at which cumulative frequency is 50. - Quartiles correspond to cumulative frequencies at 25 (Q1) and 75 (Q3). 3. **Estimating the median:** From the graph, median is the time $t$ where cumulative frequency = 50. - The curve reaches 50 students approximately at $t = 8$ minutes. So, median $= 8$ minutes. 4. **Estimating the interquartile range (IQR):** - Q1 is the time at cumulative frequency = 25. - Q3 is the time at cumulative frequency = 75. From the graph: - Q1 is about $t = 6$ minutes. - Q3 is about $t = 11$ minutes. Therefore, $$\text{IQR} = Q3 - Q1 = 11 - 6 = 5 \text{ minutes}.$$ 5. **Number of students taking more than 11 minutes:** - At $t=11$ minutes, cumulative frequency is about 75. - Total students = 100. Number taking more than 11 minutes = $100 - 75 = 25$ students. **Final answers:** (i) Median = 8 minutes (ii) Interquartile range = 5 minutes (iii) Number of students taking more than 11 minutes = 25