The table displays the scores of students on a recent exam. Find the mean of the scores to the nearest tenth.

\begin{tabular}{|c|c|}
\hline
Score & Number of Students \\
\hline
55 & 1 \\
\hline
60 & 3 \\
\hline
65 & 9 \\
\hline
70 & 5 \\
\hline
75 & 2 \\
\hline
80 & 6 \\
\hline
85 & 5 \\
\hline
90 & 4 \\
\hline
\end{tabular}



Answer :

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].