Multiple choice

Mean of 30 observations was 56 when one number, that is 42 was misread as 24. If the mistake is corrected and each observation is multiplied by 3, what will be the new mean?

  1. 170

  2. 169.8

  3. 165.2

  4. 159.5

  5. None of these.
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B Correct answer
Explanation

Old sum = 30 * 56 = 1680. Corrected sum = 1680 - 24 + 42 = 1698. Corrected mean = 1698 / 30 = 56.6. Multiplying each observation by 3 means the new mean is 56.6 * 3 = 169.8.

AI explanation

The original sum of the 30 observations is 30 times 56 = 1680. Correcting the misread number increases this sum by 18 to 1698, making the true mean 1698 divided by 30, which is 56.6. When each observation is multiplied by 3, the new mean becomes 3 times 56.6, resulting in 169.8.

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