The mean of marks secured by 60 students in division A of class X is 64, 40 students of division B is 60 and that of 60 students of division C is 58. Find the mean of marks of the students of three divisions of Class X.
- A60.05
- B59.35
- C62.15
- D60.75
Solution & Step-by-step Explanation
To find the combined mean of the three divisions, we use the weighted mean formula:
Combined Mean=
n
1
+n
2
+n
3
n
1
M
1
+n
2
M
2
+n
3
M
3
Where:
Division A: n
1
=60, M
1
=64
Division B: n
2
=40, M
2
=60
Division C: n
3
=60, M
3
=58
Calculate the sum of marks:
Total Marks=(60×64)+(40×60)+(60×58)
Total Marks=3840+2400+3480=9720
Calculate the total number of students:
Total Students=60+40+60=160
Calculate the overall mean:
Combined Mean=
160
9720
=
16
972
=60.75
Combined Mean=
n
1
+n
2
+n
3
n
1
M
1
+n
2
M
2
+n
3
M
3
Where:
Division A: n
1
=60, M
1
=64
Division B: n
2
=40, M
2
=60
Division C: n
3
=60, M
3
=58
Calculate the sum of marks:
Total Marks=(60×64)+(40×60)+(60×58)
Total Marks=3840+2400+3480=9720
Calculate the total number of students:
Total Students=60+40+60=160
Calculate the overall mean:
Combined Mean=
160
9720
=
16
972
=60.75