To find the mean score for the given data of test scores for 37 statistics students, we will follow these steps:
1. Identify the given data:
- There are 9 students who scored 90.
- There are 15 students who scored 80.
- There are 13 students who scored 70.
2. Calculate the total number of students:
[tex]\[
9 + 15 + 13 = 37
\][/tex]
The total number of students is 37.
3. Calculate the total sum of scores:
We need to multiply the number of students by their corresponding scores and then sum these products:
[tex]\[
(9 \times 90) + (15 \times 80) + (13 \times 70)
\][/tex]
Breaking it down:
[tex]\[
9 \times 90 = 810
\][/tex]
[tex]\[
15 \times 80 = 1200
\][/tex]
[tex]\[
13 \times 70 = 910
\][/tex]
Now, add these products:
[tex]\[
810 + 1200 + 910 = 2920
\][/tex]
The total sum of scores is 2920.
4. Calculate the mean score:
The mean score is found by dividing the total sum of scores by the total number of students:
[tex]\[
\text{Mean Score} = \frac{\text{Total Sum of Scores}}{\text{Total Number of Students}}
\][/tex]
Plugging in the values we found:
[tex]\[
\text{Mean Score} = \frac{2920}{37} \approx 78.9
\][/tex]
The mean score is approximately 78.9.
So, after following these steps, we find that the mean score for the statistics test is 78.9.
