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:

Given

• Batch sizes: 55, 60, 45 students
• Respective averages: 50, 55, 60

Step 1: Convert each average to a totalTotal₁ = 55 × 50 = 2750Total₂ = 60 × 55 = 3300Total₃ = 45 × 60 = 2700

Step 2: Aggregate and divide by total headcountGrand total = 2750 + 3300 + 2700 = 8750Total students = 55 + 60 + 45 = 160Overall average = 8750 ÷ 160 = 54.6875 ≈ 54.69

Why not simple averaging?

• A direct average of 50, 55, and 60 would ignore the different batch sizes; weighted average is required.

Final AnswerAverage marks of all students ≈ 54.69.