Apples Mean
1. The problem states there are 12 bags of apples, with a mean of 8 apples per bag.
2. Using the formula for mean: $$\text{mean} = \frac{\text{total apples}}{\text{number of bags}}$$ we know $$8 = \frac{\text{total apples}}{12}$$ so $$\text{total apples} = 8 \times 12 = 96$$.
3. The table gives the distribution of apples in 11 bags:
- Number of apples 6 appears 1 time, contributing $$6 \times 1 = 6$$ apples
- Number of apples 7 appears 4 times, contributing $$7 \times 4 = 28$$ apples
- Number of apples 8 appears 2 times, contributing $$8 \times 2 = 16$$ apples
- Number of apples 9 appears 3 times, contributing $$9 \times 3 = 27$$ apples
- Number of apples 10 appears 1 time, contributing $$10 \times 1 = 10$$ apples
4. Summing these apples gives the total apples in 11 bags:
$$6 + 28 + 16 + 27 + 10 = 87$$.
5. Since the total apples in all 12 bags is 96, the number of apples in the 12th bag is:
$$96 - 87 = 9$$.
6. **Final answer:** The 12th bag contains 9 apples.