To find the mean of the scores to the nearest tenth, follow these steps:
1. List the scores and the corresponding number of students:
| Score | Number of Students |
|-------|---------------------|
| 70 | 1 |
| 75 | 7 |
| 80 | 2 |
| 85 | 6 |
| 90 | 4 |
| 95 | 1 |
| 100 | 4 |
2. Calculate the total number of students:
- Add up all the numbers in the 'Number of Students' column.
- [tex]\( 1 + 7 + 2 + 6 + 4 + 1 + 4 = 25 \)[/tex]
So, the total number of students is 25.
3. Calculate the weighted sum of the scores:
- Multiply each score by the number of students who received that score, and then sum the results.
- [tex]\( (70 \times 1) + (75 \times 7) + (80 \times 2) + (85 \times 6) + (90 \times 4) + (95 \times 1) + (100 \times 4) = 70 + 525 + 160 + 510 + 360 + 95 + 400 = 2120 \)[/tex]
So, the weighted sum of the scores is 2120.
4. Calculate the mean score:
- Divide the weighted sum of the scores by the total number of students.
- [tex]\( \text{Mean} = \frac{2120}{25} = 84.8 \)[/tex]
5. Round the mean score to the nearest tenth:
- The mean score is already calculated to the nearest tenth as [tex]\( 84.8 \)[/tex].
Therefore, the mean of the scores to the nearest tenth is 84.8.
