To find the mean of the scores to the nearest tenth, we need to follow these steps:
1. Identify the Scores and the Number of Students for Each Score:
- Score: 70, Number of Students: 5
- Score: 75, Number of Students: 7
- Score: 80, Number of Students: 5
- Score: 85, Number of Students: 8
- Score: 90, Number of Students: 4
2. Calculate the Total Number of Students:
Add the number of students for each score:
[tex]\[
5 + 7 + 5 + 8 + 4 = 29
\][/tex]
3. Calculate the Weighted Sum of Scores:
Multiply each score by the number of students who received that score, and then sum those products:
- [tex]\(70 \times 5 = 350\)[/tex]
- [tex]\(75 \times 7 = 525\)[/tex]
- [tex]\(80 \times 5 = 400\)[/tex]
- [tex]\(85 \times 8 = 680\)[/tex]
- [tex]\(90 \times 4 = 360\)[/tex]
Now, add these products together to get the weighted sum:
[tex]\[
350 + 525 + 400 + 680 + 360 = 2315
\][/tex]
4. Calculate the Mean Score:
Divide the weighted sum by the total number of students:
[tex]\[
\text{Mean Score} = \frac{2315}{29} \approx 79.82758620689656
\][/tex]
5. Round the Mean Score to the Nearest Tenth:
To round to the nearest tenth, we look at the hundredths place (which is 2 in this case). Since it is less than 5, we round down.
[tex]\[
79.8
\][/tex]
Therefore, the mean of the scores to the nearest tenth is [tex]\(\boxed{79.8}\)[/tex].
