To find the mean of the scores, follow these steps:
1. Identify the scores and their frequencies: We are given a table of scores and the number of students who achieved those scores.
| Score | Number of Students |
|-------|--------------------|
| 55 | 1 |
| 60 | 3 |
| 65 | 9 |
| 70 | 5 |
| 75 | 2 |
| 80 | 6 |
| 85 | 5 |
| 90 | 4 |
2. Calculate the total score: Multiply each score by the number of students who achieved that score and then add all these products together.
[tex]\[
\begin{align*}
55 \times 1 &= 55 \\
60 \times 3 &= 180 \\
65 \times 9 &= 585 \\
70 \times 5 &= 350 \\
75 \times 2 &= 150 \\
80 \times 6 &= 480 \\
85 \times 5 &= 425 \\
90 \times 4 &= 360 \\
\end{align*}
\][/tex]
Summing these products:
[tex]\[
55 + 180 + 585 + 350 + 150 + 480 + 425 + 360 = 2585
\][/tex]
3. Calculate the total number of students: Add the number of students for each score.
[tex]\[
1 + 3 + 9 + 5 + 2 + 6 + 5 + 4 = 35
\][/tex]
4. Calculate the mean score: Divide the total score by the total number of students.
[tex]\[
\frac{2585}{35} = 73.8571 \approx 73.9
\][/tex]
5. Round the mean to the nearest 1 decimal place: The mean score, rounded to the nearest tenth, is [tex]\( 73.9 \)[/tex].
Thus, the mean of the scores is [tex]\( 73.9 \)[/tex].
