Question

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. Overall, what was the approximate mean score for all of the students on the quiz?

A. 85.7
B. 85.0
C. none of these
D. 84.3
E. It cannot be determined

Answer 1

Answer: A. 85.7

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 ,
`\text{Mean}=\frac{\text{Sum of observations}}{\text{No. of observations}}`

Then , for section A :

`\text{Mean score }=\frac{\text{Sum of scores in sec A}}{\text{No. of students}}`

`\Rightarrow\ 80=\frac{\text{Sum of scores in sec A}}{15}\\\\\Rightarrow\ \text{Sum of scores in sec A}=80*15=1200`

Similarly in Section B,
`\text{Sum of scores in sec B}=90*20=1800`

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 =
`\frac{\text{Total score}}{\text{Total students}}`

`=(3000)/(35)=85.7142857143\approx85.7`

Hence, the approximate mean score for all of the students on the quiz = 85.7

Thus , the correct answer is option A. 85.7.