1. **State the problem:** We have a set of homework marks: 5, 6, 7, 8 with frequencies 1, 3, 1, and 5 respectively. We need to find: (i) the range (ii) the mode (iii) the median (iv) the mean 2. **Recall formulas and definitions:** - Range = maximum value - minimum value - Mode = value with highest frequency - Median = middle value when data is ordered - Mean = sum of all values divided by total number of values 3. **Calculate total number of data points:** Total frequency = 1 + 3 + 1 + 5 = 10 4. **Calculate the range:** Range = max mark - min mark = 8 - 5 = 3 5. **Find the mode:** The highest frequency is 5 for mark 8, so mode = 8 6. **Find the median:** Order the data points: - One 5 - Three 6's - One 7 - Five 8's Positions 1 to 10: 1:5 2-4:6 5:7 6-10:8 Median position = $\frac{10+1}{2} = 5.5$, so median is average of 5th and 6th values. 5th value = 7 6th value = 8 Median = $\frac{7 + 8}{2} = 7.5$ 7. **Calculate the mean:** Sum = $5\times1 + 6\times3 + 7\times1 + 8\times5 = 5 + 18 + 7 + 40 = 70$ Mean = $\frac{70}{10} = 7$ **Final answers:** (i) Range = 3 (ii) Mode = 8 (iii) Median = 7.5 (iv) Mean = 7