1. **State the problem:** We have a sample of $n=6$ scores with a mean $M=10$. One score $X=12$ is removed. We need to find the new mean. 2. **Recall the formula for mean:** $$M = \frac{\text{sum of all scores}}{n}$$ 3. **Calculate the sum of all scores:** $$\text{sum} = M \times n = 10 \times 6 = 60$$ 4. **Remove the score $X=12$ from the sum:** $$\text{new sum} = 60 - 12 = 48$$ 5. **Calculate the new number of scores:** $$\text{new } n = 6 - 1 = 5$$ 6. **Calculate the new mean:** $$\text{new mean} = \frac{\text{new sum}}{\text{new } n} = \frac{48}{5}$$ 7. **Simplify the fraction:** $$\frac{48}{5} = 9.6$$ **Final answer:** The new mean is $9.6$.