To find the mean score of the quiz given the scores and their corresponding frequencies, we need to calculate the weighted sum of the scores and then divide that by the total number of students. Here's a step-by-step guide to how this can be achieved:
1. List the given scores and their corresponding frequencies:
| Score | 5 | 6 | 7 | 8 | 9 | 10 |
|---------|---|---|---|---|---|----|
| Frequency | 1 | 2 | 5 | 5 | 7 | 10 |
2. Calculate the weighted sum of the scores:
- Multiply each score by its frequency and then sum these products.
[tex]\[
\text{Weighted Sum} = (5 \times 1) + (6 \times 2) + (7 \times 5) + (8 \times 5) + (9 \times 7) + (10 \times 10)
\][/tex]
Breaking this down:
[tex]\[
= 5 + 12 + 35 + 40 + 63 + 100
\][/tex]
Adding these together:
[tex]\[
= 5 + 12 + 35 + 40 + 63 + 100 = 255
\][/tex]
3. Calculate the total number of students:
- Sum all the frequencies.
[tex]\[
\text{Total Students} = 1 + 2 + 5 + 5 + 7 + 10 = 30
\][/tex]
4. Calculate the mean score:
- Divide the weighted sum by the total number of students.
[tex]\[
\text{Mean Score} = \frac{\text{Weighted Sum}}{\text{Total Students}} = \frac{255}{30} = 8.5
\][/tex]
Therefore, the mean score on the quiz is [tex]\( \boxed{8.5} \)[/tex].
