To find the mean of the scores, we need to follow several steps:
1. List the Scores and Corresponding Number of Students:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Score} & \text{Number of Students} \\
\hline
75 & 2 \\
\hline
80 & 3 \\
\hline
85 & 9 \\
\hline
90 & 8 \\
\hline
95 & 9 \\
\hline
\end{array}
\][/tex]
2. Calculate the Total Number of Students:
[tex]\[
\text{Total Number of Students} = 2 + 3 + 9 + 8 + 9 = 31
\][/tex]
3. Calculate the Total Score:
We find the total score by multiplying each score by the number of students who received that score and then summing the results.
[tex]\[
\begin{align*}
\text{Total Score} &= (75 \times 2) + (80 \times 3) + (85 \times 9) + (90 \times 8) + (95 \times 9) \\
&= 150 + 240 + 765 + 720 + 855 \\
&= 2730
\end{align*}
\][/tex]
4. Calculate the Mean Score:
The mean score is calculated by dividing the total score by the total number of students.
[tex]\[
\text{Mean Score} = \frac{\text{Total Score}}{\text{Total Number of Students}} = \frac{2730}{31} \approx 88.06451612903226
\][/tex]
5. Round the Mean Score to the Nearest Tenth:
To round the mean score to the nearest tenth, we look at the first decimal place.
[tex]\[
\text{Mean Score to the Nearest Tenth} \approx 88.1
\][/tex]
Therefore, the mean of the scores, rounded to the nearest tenth, is [tex]\( \boxed{88.1} \)[/tex].
