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The average marks in mathematics scored by the students of a school at the public examination were 39. If four of these students who actually scored 5, 12, 15 and 19 marks at the examination had not been sent up, the average marks for the school would have been 44. Find the number of students sent up for examination from the school?

Correct answer: B. 25

  • A. 20
  • B. 25
  • C. 30
  • D. 32

Explanation

If n students were sent up, their total marks were 39n marks. Removing four students removes 5 + 12 + 15 + 19 = 51 marks, and the remaining n - 4 students have total 44(n - 4) marks, so 39n - 51 = 44(n - 4). Solving gives 5n = 125 and n = 25 students. The likely trap is 30 students, which can result from ignoring that both the total marks and the number of students change.

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An average represents the total of a set of values divided by the number of values, and a weighted average gives different importance to different groups. Problems involve missing values, combined averages, replacement of observations, and changes in the average, so the total and count must be tracked separately.

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