1. **State the problem:** Given the scores and their frequencies: Scores: $5, 6, 7, 8, 9$ Frequencies: $13, 22, 35, 26, 11$ We need to find the mean, median, mode, and range of the data. 2. **Calculate the mean:** The mean is the weighted average of the scores: $$\text{Mean} = \frac{\sum (\text{score} \times \text{frequency})}{\sum \text{frequency}}$$ Calculate numerator: $$5 \times 13 = 65$$ $$6 \times 22 = 132$$ $$7 \times 35 = 245$$ $$8 \times 26 = 208$$ $$9 \times 11 = 99$$ Sum numerator: $$65 + 132 + 245 + 208 + 99 = 749$$ Sum frequencies: $$13 + 22 + 35 + 26 + 11 = 107$$ Mean: $$\frac{749}{107} \approx 7.0$$ 3. **Calculate the median:** Total frequency is 107, so median position is at $\frac{107 + 1}{2} = 54$th value. Cumulative frequencies: - Up to score 5: 13 - Up to score 6: 13 + 22 = 35 - Up to score 7: 35 + 35 = 70 Since 54 is between 36 and 70, the median score is 7. 4. **Calculate the mode:** The mode is the score with the highest frequency. Frequencies: 13, 22, 35, 26, 11 Highest frequency is 35 at score 7. Mode = 7 5. **Calculate the range:** Range = highest score - lowest score = $9 - 5 = 4$ **Final answers:** - Mean = 7.0 - Median = 7 - Mode = 7 - Range = 4