To find the mean of the scores, we need to follow a few steps:
1. Calculate the total score: Multiply each score by the number of students who received that score, then sum all these products.
2. Calculate the total number of students: Sum the number of students who received each score.
3. Calculate the mean score: Divide the total score by the total number of students.
4. Round the mean score to the nearest 10th.
Let's dive into each step:
### Step 1: Calculate the total score
We can use the data from the table:
- For the score of 60, there are 7 students: [tex]\( 60 \times 7 = 420 \)[/tex]
- For the score of 65, there are 5 students: [tex]\( 65 \times 5 = 325 \)[/tex]
- For the score of 70, there are 3 students: [tex]\( 70 \times 3 = 210 \)[/tex]
- For the score of 75, there is 1 student: [tex]\( 75 \times 1 = 75 \)[/tex]
- For the score of 80, there are 8 students: [tex]\( 80 \times 8 = 640 \)[/tex]
- For the score of 85, there are 8 students: [tex]\( 85 \times 8 = 680 \)[/tex]
- For the score of 90, there are 4 students: [tex]\( 90 \times 4 = 360 \)[/tex]
Now, sum these products to find the total score:
[tex]\[ 420 + 325 + 210 + 75 + 640 + 680 + 360 = 2710 \][/tex]
### Step 2: Calculate the total number of students
Sum the number of students for each score:
[tex]\[ 7 + 5 + 3 + 1 + 8 + 8 + 4 = 36 \][/tex]
### Step 3: Calculate the mean score
Divide the total score by the total number of students:
[tex]\[ \frac{2710}{36} \approx 75.27777777777777 \][/tex]
### Step 4: Round the mean score to the nearest 10th
The mean score to the nearest 10th is [tex]\( 75.3 \)[/tex].
### Conclusion
The mean score of the students on the exam, rounded to the nearest 10th, is [tex]\( 75.3 \)[/tex].
