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The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years. The age of the 15th student is____________?

Correct answer: A. 11 years

  • A. 11 years
  • B. 14 years
  • C. 15 years
  • D. 15 2/7 years

Explanation

The total age of all 15 students is 15 x 15 = 225 years. The 5 students contribute 5 x 14 = 70 years and the other 9 contribute 9 x 16 = 144 years, leaving 225 - 70 - 144 = 11 years for the fifteenth student. A student may choose 14 years by confusing the given average of the five students with the missing student's age.

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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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