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The average weight of 16 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg. Find the average weights of all the boys in the class.

Correct answer: C. 48.55 kg

  • A. 47.55 kg
  • B. 48 kg
  • C. 48.55 kg
  • D. 49.25 kg

Explanation

The total weight of the 16 boys is 16 x 50.25 kg = 804 kg, and that of the 8 remaining boys is 8 x 45.15 kg = 361.2 kg. Thus total weight is 1165.2 kg and the average is 1165.2 kg ÷ 24 boys = 48.55 kg. The likely mistake is option a, which gives too much weight to the lower average of the smaller group.

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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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