To solve the problem and determine the number of apples in the 12th bag, we need to follow a few clear steps:
1. Calculate the total number of apples across all 12 bags:
- We are given that the mean number of apples per bag is 8.
- There are 12 bags in total.
[tex]\[
\text{Total number of apples} = \text{mean number of apples per bag} \times \text{number of bags} = 8 \times 12 = 96
\][/tex]
2. Calculate the sum of apples in the 11 bags:
- The table provides the number of apples in 11 bags as follows:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Number of apples} & \text{Frequency} \\
\hline 6 & 1 \\
\hline 7 & 4 \\
\hline 8 & 2 \\
\hline 9 & 3 \\
\hline 10 & 1 \\
\hline
\end{array}
\][/tex]
- We can expand the table to list each bag's apple count: [tex]\( [6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 10] \)[/tex]
- Now sum these values:
[tex]\[
6 + 7 + 7 + 7 + 7 + 8 + 8 + 9 + 9 + 9 + 10 = 87
\][/tex]
3. Determine the number of apples in the 12th bag:
- We know the total number of apples across all 12 bags is 96, and the sum of apples in the first 11 bags is 87.
- Subtract the total apples in 11 bags from the total apples in all 12 bags to find the apples in the 12th bag:
[tex]\[
\text{Number of apples in 12th bag} = \text{Total apples in all bags} - \text{Total apples in 11 bags} = 96 - 87 = 9
\][/tex]
So, the number of apples in the 12th bag is [tex]\( \boxed{9} \)[/tex].
