Answer: A. 85.7
Step-by-step explanation:
Given : Two sections of a class took the same quiz.
Section A had 15 students who had a mean score of 80, and Section B had 20 students who had a mean score of 90.
We know that , [tex]\text{Mean}=\dfrac{\text{Sum of observations}}{\text{No. of observations}}[/tex]
Then , for section A :
[tex]\text{Mean score }=\dfrac{\text{Sum of scores in sec A}}{\text{No. of students}}[/tex]
[tex]\Rightarrow\ 80=\dfrac{\text{Sum of scores in sec A}}{15}\\\\\Rightarrow\ \text{Sum of scores in sec A}=80\times15=1200[/tex]
Similarly in Section B, [tex]\text{Sum of scores in sec B}=90\times20=1800[/tex]
Total scores = Sum of scores in sec A+Sum of scores in sec B
=1200+1800=3000
Total students = Students in sec A +Students in sec B
=15+20=35
Now , the mean score for all of the students on the quiz =[tex]\dfrac{\text{Total score}}{\text{Total students}}[/tex]
[tex]=\dfrac{3000}{35}=85.7142857143\approx85.7[/tex]
Hence, the approximate mean score for all of the students on the quiz = 85.7
Thus , the correct answer is option A. 85.7.
