The average of the marks of 12 students in a class is 68. If the marks of each…

Concept: When every value in a data set is multiplied by the same constant k, the new average equals k times the original average. This holds because the new sum equals k times the original sum (new sum = k × original sum), while the number of values (n) stays unchanged, so new average = new sum / n = k × (original sum / n) = k × original average.

1. The original average is A = 68 for n = 12 students, so the original total of all marks is S = A × n = 68 × 12 = 816.

2. Every student's marks are doubled (k = 2), so the new total becomes S' = 2 × S = 2 × 816 = 1632.

3. The number of students is unchanged at n = 12, so the new average is S' / n = 1632 / 12 = 136.

Cross-check: take a smaller sample with the same average — two students scoring 60 and 76 have average (60 + 76) / 2 = 68. Doubling each mark gives 120 and 152, whose average is (120 + 152) / 2 = 136, matching 2 × 68 = 136 and confirming the rule.

So the new average of the class is 136.