To calculate the mean score of the students on the recent exam and round it to the nearest 10th, follow these steps:
1. Identify the Scores and the Number of Students:
| Score | Number of Students |
|-------|--------------------|
| 75 | 1 |
| 80 | 2 |
| 85 | 8 |
| 90 | 3 |
| 95 | 9 |
2. Calculate the Total Number of Students:
Sum all the numbers in the "Number of Students" column:
[tex]\[
1 + 2 + 8 + 3 + 9 = 23
\][/tex]
So, the total number of students is 23.
3. Calculate the Total Scores:
Multiply each score by the number of students who received that score, then sum all these products:
[tex]\[
(75 \times 1) + (80 \times 2) + (85 \times 8) + (90 \times 3) + (95 \times 9)
\][/tex]
Doing the calculations:
[tex]\[
75 \times 1 = 75
\][/tex]
[tex]\[
80 \times 2 = 160
\][/tex]
[tex]\[
85 \times 8 = 680
\][/tex]
[tex]\[
90 \times 3 = 270
\][/tex]
[tex]\[
95 \times 9 = 855
\][/tex]
Adding these results together:
[tex]\[
75 + 160 + 680 + 270 + 855 = 2040
\][/tex]
So, the total scores sum up to 2040.
4. Calculate the Mean Score:
Divide the total scores by the total number of students:
[tex]\[
\text{Mean Score} = \frac{\text{Total Scores}}{\text{Total Number of Students}} = \frac{2040}{23} \approx 88.69565217391305
\][/tex]
5. Round the Mean Score to the Nearest 10th:
The result from the division is approximately 88.69565217391305. When rounding to the nearest 10th:
[tex]\[
88.69565217391305 \approx 88.7
\][/tex]
Therefore, the mean score of the students on the exam, rounded to the nearest 10th, is 88.7.
