To find the number of apples in the 12th bag, follow these steps:
1. Calculate the total number of apples in the first 11 bags:
- We use the table to identify the number of apples in each bag and their corresponding frequencies:
[tex]\[
\begin{aligned}
&\text{Number of apples in 6-apple bags} &= 6 \times 1 &= 6 \\
&\text{Number of apples in 7-apple bags} &= 7 \times 4 &= 28 \\
&\text{Number of apples in 8-apple bags} &= 8 \times 2 &= 16 \\
&\text{Number of apples in 9-apple bags} &= 9 \times 3 &= 27 \\
&\text{Number of apples in 10-apple bags} &= 10 \times 1 &= 10 \\
\end{aligned}
\][/tex]
- Sum these amounts to find the total number of apples in the first 11 bags:
[tex]\[
6 + 28 + 16 + 27 + 10 = 87
\][/tex]
2. Calculate the total number of apples in all 12 bags using the mean:
- The mean number of apples per bag is given as 8. Therefore, the total number of apples in all 12 bags is:
[tex]\[
8 \times 12 = 96
\][/tex]
3. Determine the number of apples in the 12th bag:
- To find the number of apples in the 12th bag, subtract the total number of apples in the first 11 bags from the overall total number of apples:
[tex]\[
96 - 87 = 9
\][/tex]
Thus, the number of apples in the 12th bag is [tex]\( 9 \)[/tex].
