1. **State the problem:** We have scores 4, 5, 6, 7, 8 with frequencies 2, 3, 9, b, and 1 respectively. The mean score is 6. We need to find the value of b. 2. **Recall the formula for mean:** $$\text{Mean} = \frac{\sum (\text{score} \times \text{frequency})}{\sum \text{frequency}}$$ 3. **Calculate the total frequency:** $$2 + 3 + 9 + b + 1 = 15 + b$$ 4. **Calculate the sum of score times frequency:** $$4 \times 2 + 5 \times 3 + 6 \times 9 + 7 \times b + 8 \times 1 = 8 + 15 + 54 + 7b + 8 = 85 + 7b$$ 5. **Set up the equation using the mean:** $$6 = \frac{85 + 7b}{15 + b}$$ 6. **Multiply both sides by the denominator:** $$6(15 + b) = 85 + 7b$$ 7. **Expand the left side:** $$90 + 6b = 85 + 7b$$ 8. **Rearrange to isolate b:** $$90 - 85 = 7b - 6b$$ $$5 = b$$ 9. **Conclusion:** The value of b is 5.