To find the mean of the scores to the nearest tenth, we will follow these steps:
1. Determine the total weighted score:
- Multiply each score by the number of students who received that score.
- Sum all these products to get the total weighted score.
2. Calculate the total number of students:
- Sum the total number of students.
3. Find the mean score:
- Divide the total weighted score by the total number of students.
4. Round the mean score to the nearest tenth.
Let's break this down step by step:
### Step 1: Calculate the total weighted score
For each score:
- [tex]\( 55 \times 2 = 110 \)[/tex]
- [tex]\( 60 \times 1 = 60 \)[/tex]
- [tex]\( 65 \times 5 = 325 \)[/tex]
- [tex]\( 70 \times 8 = 560 \)[/tex]
- [tex]\( 75 \times 1 = 75 \)[/tex]
- [tex]\( 80 \times 5 = 400 \)[/tex]
- [tex]\( 85 \times 7 = 595 \)[/tex]
- [tex]\( 90 \times 5 = 450 \)[/tex]
Adding these all together:
[tex]\[ 110 + 60 + 325 + 560 + 75 + 400 + 595 + 450 = 2575 \][/tex]
So, the total weighted score is [tex]\( 2575 \)[/tex].
### Step 2: Calculate the total number of students
Adding the number of students:
[tex]\[ 2 + 1 + 5 + 8 + 1 + 5 + 7 + 5 = 34 \][/tex]
So, the total number of students is [tex]\( 34 \)[/tex].
### Step 3: Calculate the mean score
The mean score is calculated by dividing the total weighted score by the total number of students:
[tex]\[ \text{Mean Score} = \frac{2575}{34} \approx 75.73529411764706 \][/tex]
### Step 4: Round the mean score to the nearest tenth
Rounding [tex]\( 75.73529411764706 \)[/tex] to the nearest tenth:
[tex]\[ 75.7 \][/tex]
Thus, the mean score of the students to the nearest tenth is [tex]\( 75.7 \)[/tex].
