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CA Foundation · Quantitative Aptitude · Measures of Central Tendency and Dispersion

The mean of 20 observations was calculated as 45. It was later found that one observation 38 was wrongly recorded as 83. What is the correct mean?

The correct mean is 42.75. The wrongly computed total is 20 × 45 = 900. Replacing 83 with 38 reduces it by 45 to 855. Dividing 855 by 20 gives 42.75. Because the wrong entry was too high, the mean must fall.

  1. A42.75Correct
  2. B47.25
  3. C45.00
  4. D40.50

Explanation

Wrong total = 20 × 45 = 900. Correct total = 900 − 83 + 38 = 855. Correct mean = 855/20 = 42.75. Check: the error of 45 spread over 20 items is 2.25, and 45 − 2.25 = 42.75. The option 47.25 adds the 2.25 instead of subtracting it.

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