1. **Problem statement:** Daisy recorded her 50 homework marks with frequencies given for each mark from 15 to 20. We need to find: (i) The range (ii) The mode (iii) The median (iv) The mean 2. **Given data:** Homework marks: 15, 16, 17, 18, 19, 20 Frequencies: 1, 3, 19, 11, 10, 6 3. **(i) Range:** The range is the difference between the highest and lowest marks. $$\text{Range} = 20 - 15 = 5$$ 4. **(ii) Mode:** The mode is the mark with the highest frequency. Frequencies: 1, 3, 19, 11, 10, 6 Highest frequency is 19 at mark 17. So, $$\text{Mode} = 17$$ 5. **(iii) Median:** The median is the middle value when all marks are arranged in order. Total frequency = 1 + 3 + 19 + 11 + 10 + 6 = 50 Median position = $$\frac{50 + 1}{2} = 25.5$$th value Cumulative frequencies: - Up to 15: 1 - Up to 16: 1 + 3 = 4 - Up to 17: 4 + 19 = 23 - Up to 18: 23 + 11 = 34 The 25.5th value lies in the 18 marks group (since 23 < 25.5 ≤ 34). So, $$\text{Median} = 18$$ 6. **(iv) Mean:** Mean is the sum of all marks times their frequencies divided by total frequency. Calculate total sum: $$\text{Sum} = 15 \times 1 + 16 \times 3 + 17 \times 19 + 18 \times 11 + 19 \times 10 + 20 \times 6$$ $$= 15 + 48 + 323 + 198 + 190 + 120 = 894$$ Mean: $$\text{Mean} = \frac{894}{50} = 17.88$$ --- **Summary:** (i) Range = 5 (ii) Mode = 17 (iii) Median = 18 (iv) Mean = 17.88