1. **State the problem:** We have a bar chart showing the frequency of spelling test scores from 6 to 10. The frequencies for scores 6, 7, 8, and 10 are 2, 3, 5, and 1 respectively, and the frequency for score 9 is unknown. The mean score is given as 8. We need to find the frequency (height of the bar) for score 9. 2. **Recall the formula for the mean:** $$\text{Mean} = \frac{\sum (\text{score} \times \text{frequency})}{\sum \text{frequency}}$$ 3. **Set up the equation:** Let the unknown frequency for score 9 be $x$. Sum of frequencies: $$2 + 3 + 5 + x + 1 = 11 + x$$ Sum of score times frequency: $$6 \times 2 + 7 \times 3 + 8 \times 5 + 9 \times x + 10 \times 1 = 12 + 21 + 40 + 9x + 10 = 83 + 9x$$ 4. **Use the mean formula:** $$8 = \frac{83 + 9x}{11 + x}$$ 5. **Solve for $x$:** Multiply both sides by $11 + x$: $$8(11 + x) = 83 + 9x$$ $$88 + 8x = 83 + 9x$$ Subtract $8x$ from both sides: $$88 = 83 + x$$ Subtract 83 from both sides: $$88 - 83 = x$$ $$5 = x$$ 6. **Interpretation:** The frequency for score 9 should be 5. **Final answer:** The bar representing a score of 9 should have a height of 5.