In a class, the average marks of 12 students is 36. If each student's marks…

Concept

The average (mean) of a set of values equals the sum of the values divided by the number of values. A key scaling property follows directly: if every value in the set is multiplied by the same constant k, the sum is also multiplied by k, so the average is multiplied by that same constant k.

Application

1. The original average of 12 students is 36, so the total marks of all 12 students = 12 × 36 = 432.

2. Each student's marks are doubled, so the new total marks = 2 × 432 = 864.

3. New average = new total marks ÷ number of students = 864 ÷ 12 = 72.

Cross-check

Cross-check using the scaling property directly: new average = 2 × old average = 2 × 36 = 72, which matches the result above.