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The average runs scored by a batsman in 20 matches is 40. In the next 10 matches the batsman scored an average of 13 runs. Find his average in all the 30 matches?

Correct answer: A. 31

  • A. 31
  • B. 29
  • C. 28
  • D. 30

Explanation

In the first 20 matches, the batsman scored 20 × 40 = 800 runs. In the next 10 matches, he scored 10 × 13 = 130 runs, making 930 runs in 30 matches. His overall average is 930 runs / 30 matches = 31 runs per match. The likely mistake is averaging 40 runs and 13 runs directly, which ignores that the two periods contain different numbers of matches.

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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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