A class of 68 students made a mean score of 60 marks and another class of 32 students made it exactly 52.5. What is the overall mean score?
- A53.5
- B54.3
- C56.2
- D57.6
Solution & Step-by-step Explanation
We can use the weighted mean formula:
Overall Mean=
n
1
+n
2
n
1
μ
1
+n
2
μ
2
Given:
n
1
=68, μ
1
=60
n
2
=32, μ
2
=52.5
Total Marks=(68×60)+(32×52.5)
68×60=4080
32×52.5=1680
Total Marks=4080+1680=5760
Total number of students = 68+32=100
Overall Mean=
100
5760
=57.6
Overall Mean=
n
1
+n
2
n
1
μ
1
+n
2
μ
2
Given:
n
1
=68, μ
1
=60
n
2
=32, μ
2
=52.5
Total Marks=(68×60)+(32×52.5)
68×60=4080
32×52.5=1680
Total Marks=4080+1680=5760
Total number of students = 68+32=100
Overall Mean=
100
5760
=57.6