To find the number of apples in the 13th bag, we need to follow a systematic approach, as outlined below:
1. Determine the total number of bags and the mean number of apples per bag:
- Number of bags: [tex]\(13\)[/tex]
- Mean number of apples per bag: [tex]\(6\)[/tex]
2. Calculate the total number of apples required for all 13 bags:
Since the mean is calculated as the total number of apples divided by the number of bags, we can write:
[tex]\[
\text{Total number of apples} = \text{Mean} \times \text{Number of bags}
\][/tex]
Substituting the given values:
[tex]\[
\text{Total number of apples} = 6 \times 13 = 78
\][/tex]
3. Sum the number of apples in the 12 given bags:
The table shows the number of apples in the 12 of the bags:
[tex]\[
4, 5, 6, 7, 8, 6, 5, 6, 7, 8, 6, 7
\][/tex]
Let's add these up:
[tex]\[
4 + 5 + 6 + 7 + 8 + 6 + 5 + 6 + 7 + 8 + 6 + 7 = 75
\][/tex]
4. Calculate the number of apples in the 13th bag:
To find the number of apples in the 13th bag, we subtract the total number of apples in the 12 bags from the total number of apples required for all 13 bags:
[tex]\[
\text{Apples in 13th bag} = \text{Total number of apples required} - \text{Total number of apples in 12 bags}
\][/tex]
Substituting the values we have:
[tex]\[
\text{Apples in 13th bag} = 78 - 75 = 3
\][/tex]
Therefore, the number of apples in the 13th bag is [tex]\(3\)[/tex].
