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The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is___________?

Correct answer: C. 51.4 approx.

  • A. 45
  • B. 50
  • C. 51.4 approx.
  • D. 54.6 approx.

Explanation

Use a weighted average: the top 20% contribute 0.20 x 80 = 16 points and the bottom 25% contribute 0.25 x 31 = 7.75 points to the overall average of 52. Thus 0.55 x = 52 - 16 - 7.75 = 28.25, so x = 28.25 / 0.55 = 51.36, approximately 51.4. A student may choose 50 by averaging the three group means directly, but the groups are unequal in size.

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About Averages

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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