To find the mean of the marks scored by the students, we follow these steps:
1. Identify the marks and the number of students for each mark category:
The given marks and the corresponding number of students are:
- Marks: 1, 2, 3, 4, and 5
- Number of students: 4, 7, 10, 11, and 8
2. Calculate the total number of students:
Sum the number of students in each category:
[tex]\[
\text{Total number of students} = 4 + 7 + 10 + 11 + 8 = 40
\][/tex]
3. Calculate the weighted sum of the marks:
Multiply each mark by the number of students who scored that mark and sum the results:
[tex]\[
\text{Weighted sum} = (1 \times 4) + (2 \times 7) + (3 \times 10) + (4 \times 11) + (5 \times 8)
\][/tex]
[tex]\[
\text{Weighted sum} = 4 + 14 + 30 + 44 + 40 = 132
\][/tex]
4. Calculate the mean mark:
The mean is found by dividing the weighted sum by the total number of students:
[tex]\[
\text{Mean} = \frac{\text{Weighted sum}}{\text{Total number of students}} = \frac{132}{40} = 3.3
\][/tex]
5. Round the mean to two decimal places:
Since the mean calculated is already appropriately precise, we have:
[tex]\[
\text{Mean (rounded to two decimal places)} = 3.3
\][/tex]
Thus, the mean mark, correct to two decimal places, is [tex]\(3.3\)[/tex].
