A class of 30 students appeared in a test. The average score of 12 students is 62, and that of the rest is 74. What is the average score of the class?

Correct — C. Averages cannot be averaged; turn each into a total first.

Group 1: 12 students × 62 = 744
Group 2: 30 − 12 = 18 students, and 18 × 74 = 1,332

Class total = 744 + 1,332 = 2,076
Class average = 2,076 ⁄ 30 = 69.2 → option (c).

Shortcut: the two group averages differ by 12, and the higher group holds 18⁄30 of the class, so the class average sits 12 × 18⁄30 = 7.2 above 62.

Why the others are wrong

• (a)
  67.2 — 67.2 leans the wrong way. It sits below the midpoint of 62 and 74, which would need the larger group to be the one averaging 62. Here the larger group of 18 averages the higher 74.
• (b)
  68.2 — The plain midpoint of 62 and 74 is 68, and 68.2 sits next to it. Weighting by the group sizes 12 and 18 pulls the class figure up past 68, to 69.2.
• (d)
  70.2 — 70.2 needs a class total of 2,106. The class actually scored 744 + 1,332 = 2,076, which is 30 marks fewer, and 2,076 ⁄ 30 is 69.2.

A weighted mean is the combined total divided by the combined count, and total = average × count is the step that makes two averages addable.

It always lies between the two group means, closer to the larger group. With 12 students at 62 and 18 at 74, the answer must sit above the midpoint 68 and below 74.

The deviation form does it in one line: start at the lower average and move up by the gap times the higher group's share, 62 + (18⁄30) × 12 = 69.2.

Key facts

• Total = average × count, which is what allows two averages to be combined.
• 12 × 62 = 744 and 18 × 74 = 1,332, giving a class total of 2,076.
• 2,076 ⁄ 30 = 69.2.
• Deviation form: 62 + (18⁄30) × (74 − 62) = 62 + 7.2 = 69.2.

Common traps

• Averaging the two averages to 68 and ignoring that the groups differ in size.
• Taking the second group as 30 students instead of the remaining 18.
• Dividing the combined total by 2 rather than by 30.

No directly related past PYQ was found.