To find the mean of the scores to the nearest 1 decimal place, we can follow these steps:
1. First, we need to calculate the total sum of all the scores. We do this by multiplying each score by the number of students who received that score, and then summing all these products together.
Let's compute it step-by-step:
[tex]\[
\begin{align*}
60 \times 4 &= 240 \\
65 \times 1 &= 65 \\
70 \times 7 &= 490 \\
75 \times 2 &= 150 \\
80 \times 3 &= 240 \\
85 \times 4 &= 340 \\
90 \times 7 &= 630 \\
95 \times 1 &= 95 \\
\end{align*}
\][/tex]
Now, summing these values:
[tex]\[
240 + 65 + 490 + 150 + 240 + 340 + 630 + 95 = 2250
\][/tex]
So, the total sum of all scores is [tex]\(2250\)[/tex].
2. Next, we need to calculate the total number of students. We can do this by summing the number of students who received each score:
[tex]\[
4 + 1 + 7 + 2 + 3 + 4 + 7 + 1 = 29
\][/tex]
So, the total number of students is [tex]\(29\)[/tex].
3. To find the mean score, we divide the total sum of all the scores by the total number of students:
[tex]\[
\text{Mean score} = \frac{2250}{29} \approx 77.58620689655173
\][/tex]
4. Finally, we need to round the mean score to the nearest 1 decimal place:
[tex]\[
77.58620689655173 \approx 77.6
\][/tex]
Therefore, the mean of the scores to the nearest 1 decimal place is [tex]\(77.6\)[/tex].
