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If the average marks of three batches of 55, 60 and 45 students respectively is 50, 55, 60, then the average marks of all the students is__________?

Correct answer: B. 54.68

  • A. 53.33
  • B. 54.68
  • C. 55
  • D. None of these

Explanation

Use total marks divided by total students: (55 x 50 + 60 x 55 + 45 x 60) marks = 8750 marks, and total students = 55 + 60 + 45 = 160. The combined average is 8750 marks ÷ 160 students = 54.6875 marks, approximately 54.68 marks. The likely mistake is option c, which is the simple average of the three batch averages and ignores their different sizes.

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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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