In the 8 th class, consisting of 30 students, a Mathematics test was taken. 10 students had an average score of 90. The other students had an average score of 75. What is the average score of the whole class?

Correct — C. Turn each average back into a total before you combine them.

10 students × 90 = 900
Remaining students = 30 − 10 = 20
20 × 75 = 1,500

Class total = 900 + 1,500 = 2,400
Class average = 2,400 ⁄ 30 = 80 → option (c)

Why the others are wrong

• (a)
  78 — 78 would need the class to score 2,340 marks in total. The two groups actually contribute 900 and 1,500, which is 2,400, so 78 is 60 marks light.
• (b)
  74 — 74 lies below both group averages, and a weighted mean can never fall outside the range of the values it averages. The answer has to sit between 75 and 90.
• (d)
  76 — 76 would need a total of 2,280. The 10 high scorers carry one-third of the weight, so the mean sits a third of the way from 75 up to 90 — at 80, not 76.

A class average is a weighted mean, not the average of the two group averages.

Each group pulls the answer towards itself in proportion to its size. Ten students out of thirty carry weight 1⁄3, the other twenty carry 2⁄3.

So the mean is 75 + (1⁄3)(90 − 75) = 80, a third of the way up from the lower average to the higher one.

The safe routine never changes: convert each average into a total, add the totals, divide by the combined count.

Key facts

• Combined average = sum of all values ÷ total count, never the average of the averages.
• Two groups of sizes m and n with means A and B combine to (mA + nB) ⁄ (m + n).
• A weighted mean always lies between the smallest and the largest group mean.
• Here 10 × 90 + 20 × 75 = 2,400 over 30 students, giving 80.

Common traps

• Averaging 90 and 75 to get 82.5, which ignores that the groups differ in size
• Taking the 10 students as the whole class and forgetting the other 20
• Dividing the combined total by 2 instead of by 30

No directly related past PYQ was found.