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The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 21 years and the average age of the last three persons is 34 years, then find the age of the person sitting in the middle of the row?

Correct answer: B. 31 years

  • A. 30 Years
  • B. 31 years
  • C. 26 years
  • D. 33 years

Explanation

The total age of seven persons is 7 × 28 = 196 years. The first three contribute 3 × 21 = 63 years and the last three contribute 3 × 34 = 102 years; these groups exclude only the middle person, so the middle age is 196 - 63 - 102 = 31 years. A student may choose 30 years by rounding or by averaging the two group averages instead of using the total.

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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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