Let's find the mean of the scores step-by-step:
1. Identify the data:
We have the following scores and the corresponding number of students:
- Score 65: 4 students
- Score 70: 8 students
- Score 75: 6 students
- Score 80: 3 students
- Score 85: 6 students
- Score 90: 6 students
2. Calculate the total number of students:
[tex]\[
\text{Total number of students} = 4 + 8 + 6 + 3 + 6 + 6 = 33
\][/tex]
3. Calculate the weighted sum of scores:
We need to multiply each score by the number of students who received that score and sum the results:
[tex]\[
\text{Weighted sum} = (65 \times 4) + (70 \times 8) + (75 \times 6) + (80 \times 3) + (85 \times 6) + (90 \times 6)
\][/tex]
[tex]\[
= 260 + 560 + 450 + 240 + 510 + 540 = 2560
\][/tex]
4. Calculate the mean score:
The mean score is the weighted sum divided by the total number of students:
[tex]\[
\text{Mean score} = \frac{\text{Weighted sum}}{\text{Total number of students}} = \frac{2560}{33} \approx 77.57575757575758
\][/tex]
5. Round the mean score to the nearest 10th:
When rounded to the nearest 10th, the mean score is:
[tex]\[
\text{Mean score (rounded to the nearest 10th)} = 77.6
\][/tex]
Thus, the mean of the scores to the nearest 10th is:
[tex]\[
\boxed{77.6}
\][/tex]
