To find the mean of the scores to the nearest 1/10th, let's follow these detailed steps:
1. List the Scores and the Number of Students:
- Scores: 65, 70, 75, 80, 85, 90
- Number of Students: 3, 2, 9, 4, 5, 5
2. Calculate the Total Number of Students:
- Total number of students = 3 + 2 + 9 + 4 + 5 + 5 = 28
3. Calculate the Weighted Sum of Scores:
- Multiply each score by the number of students who achieved that score:
[tex]\[
65 \times 3 + 70 \times 2 + 75 \times 9 + 80 \times 4 + 85 \times 5 + 90 \times 5
\][/tex]
- [tex]\(65 \times 3 = 195\)[/tex]
- [tex]\(70 \times 2 = 140\)[/tex]
- [tex]\(75 \times 9 = 675\)[/tex]
- [tex]\(80 \times 4 = 320\)[/tex]
- [tex]\(85 \times 5 = 425\)[/tex]
- [tex]\(90 \times 5 = 450\)[/tex]
- Summing these up gives:
[tex]\[
195 + 140 + 675 + 320 + 425 + 450 = 2205
\][/tex]
4. Calculate the Mean Score:
- Divide the weighted sum by the total number of students:
[tex]\[
\text{Mean score} = \frac{2205}{28} = 78.75
\][/tex]
5. Round the Mean Score to the Nearest 1/10th:
- The mean score, 78.75, rounded to the nearest 1/10th is 78.8.
Therefore, the mean of the scores to the nearest 1/10th is [tex]\(\boxed{78.8}\)[/tex].
