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The average of 11 results is 50, if the average of first six results is 49 and that of the last six is 52. Find the sixth result?

Correct answer: B. 56

  • A. 46
  • B. 56
  • C. 34
  • D. 57

Explanation

The total of 11 results is 11 x 50 = 550, while the first six total 6 x 49 = 294 and the last six total 6 x 52 = 312. The first-six and last-six groups overlap in the sixth result, so the sixth result is 294 + 312 - 550 = 56. The likely mistake is choosing 46 by subtracting the two group totals in the wrong way.

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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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