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

For 10 observations, the mean was calculated as 20 and the standard deviation as 5. It was later found that the value 15 had been wrongly copied as 5. What is the correct standard deviation?

The correct standard deviation is 2. Replacing 5 with 15 raises the sum to 210 (mean 21) and the sum of squares to 4450. The variance is 445 minus 441, which equals 4, so the standard deviation is 2.

  1. A2Correct
  2. B3
  3. C5
  4. D√10

Explanation

Original Σx = 200 and Σx² = 10(25 + 400) = 4250. Corrected Σx = 200 − 5 + 15 = 210, so the mean is 21. Corrected Σx² = 4250 − 25 + 225 = 4450. Variance = 445 − 441 = 4, so SD = 2. Keeping 5 ignores the correction; √10 comes from using the old mean 20 with the new Σx².

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