The mean of marks secured by 65 students in division A of class X is 54, 30 students of division B is 50 and that of 55 students of division C is 48. Find the mean of marks of the students of three divisions of Class X.

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
​

x
ˉ

1
​
+n
2
​

x
ˉ

2
​
+n
3
​

x
ˉ

3
​

​

Where:

Division A: n
1
​
=65,
x
ˉ

1
​
=54

Division B: n
2
​
=30,
x
ˉ

2
​
=50

Division C: n
3
​
=55,
x
ˉ

3
​
=48

Let's calculate the total marks across all sections:

Total marks=(65×54)+(30×50)+(55×48)
Total marks=3510+1500+2640=7650
Total number of students:

Total students=65+30+55=150
Now calculate the combined mean:

Combined Mean=
150
7650
​
=
15
765
​
=51