There are 12 bags of apples on a market stall. The mean number of apples in each bag is 8.

The table shows the number of apples in 11 of the bags. Calculate the number of apples in the 12th bag. Show your working.

\begin{tabular}{|c|c|}
\hline
\textbf{Number of apples} & \textbf{Frequency} \\
\hline
6 & 1 \\
\hline
7 & 4 \\
\hline
8 & 2 \\
\hline
9 & 3 \\
\hline
10 & 1 \\
\hline
\end{tabular}



Answer :

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].