Question

If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is:

Answer 1

The average marks of batch of 55 students is 50.

So , Total marks of batch of 55 students = average × number of students
= 55×50
= 2750

The average marks of batch of 60 students is 55.

So, total marks of batch of 60 students =
average × number of students
=60 × 55
=3300

The average marks of batch of 45 students is 60.

So, total marks of batch of 45 students =
average × number of students
= 45×60
=2700


Total Number of students = 55 + 60 + 45= 160

Total marks of students = 2750 + 3300 + 2700= 8750


Average marks of all the students =
Total marks / Total number of students.

= 8750/160
=54.6875

Answer) Average marks of all the students is 54.6875.

Answer 2

Let the batch be A, B, C with average marks 50, 55, 60 respectively.
Number of students in A, B, C be 55, 60, 45

# Average of A = Sum of marks/ Total number of students = 50
Average of A = Sum of marks/55 = 50
        sum of marks of A = 2750

# Average of B = Sum of marks/ Total number of students = 55
Average of B = Sum of marks/60 = 55
        sum of marks of B = 3300

# Average of C = Sum of marks/ Total number of students = 60
Average of C = Sum of marks/45 = 60
        sum of marks of C = 2700

Average= Total Sum of marks/ Total number of students (incl. All batches)

Total marks =2750+3300+2700 =8750
Total students= 55+60+45= 160

Average = 8750/160 =54.6875