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The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is___________?

Correct answer: C. 36.5

  • A. 35.2
  • B. 36.1
  • C. 36.5
  • D. 39.1

Explanation

The original total was 50 x 36 = 1800. Correcting an observation from 23 to 48 increases the total by 48 - 23 = 25, giving 1825, and the corrected mean is 1825 / 50 = 36.5. A student may choose 36.1 by making too small an adjustment or by dividing the correction incorrectly.

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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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