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The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is_____________?

Correct answer: D. 11.5

  • A. 11.0
  • B. 11.3
  • C. 11.4
  • D. 11.5

Explanation

The total of all 11 numbers is 11 x 10.9 = 119.9. The first six total 6 x 10.5 = 63.0, while the last six total 6 x 11.4 = 68.4; adding these includes the sixth number twice, so the sixth number is 63.0 + 68.4 - 119.9 = 11.5. The likely trap is 11.4, which uses the average of the last six instead of finding their shared number.

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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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