A class of 30 students appeared in a test. The average score of 12 students is 62, and that of the rest is 60. What is the average score of the class?

Correct — A. The two groups are unequal in size, so you must weight by headcount. Averaging 62 and 60 is not available here.

Group sizes: 12 students, and 30 − 12 = 18 students.
Total of the first group = 12 × 62 = 744
Total of the second group = 18 × 60 = 1080
Class total = 744 + 1080 = 1824

Class average = 1824 ÷ 30 = 60.8 → option (a).

Why the others are wrong

• (b)
  59.8 — Every student scored on a group average of 60 or 62, so the class mean cannot fall below 60. 59.8 sits outside the range the two group averages allow.
• (c)
  58.8 — The same impossibility, further out. A mean of 58.8 would need scores below the lower group average of 60, and no group here averages less than 60.
• (d)
  61.8 — 61.8 sits nearer 62 than 60, which would need the 62-scoring group to be the majority. It is 12 of 30, the smaller group, so the mean must land nearer 60. 61.8 would need 27 students averaging 62.

A class average is a weighted mean: each group's average counts in proportion to how many students carry it.

Adding 62 and 60 and halving gives 61, which is wrong here because the 62-group holds only 12 of the 30 places.

The safe routine is to turn every average back into a total (average × count), add the totals, then divide by the combined count. Averages are never added to each other.

Sanity check: the answer must lie strictly between the smallest and the largest group average — here strictly between 60 and 62.

Key facts

• Weighted mean = (sum of all values) ÷ (total count), so convert each average into a total before adding.
• The combined average of two groups always lies strictly between the two group averages, unless those averages are equal.
• Here the group totals are 12 × 62 = 744 and 18 × 60 = 1080, giving 1824 across 30 students.

Common traps

• Averaging 62 and 60 to get 61, which ignores that the groups are 12 and 18.
• Reading 'the rest' as another 12 students instead of 18.
• Dividing the combined total by 2 groups rather than by 30 students.

No directly related past PYQ was found.