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The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. Later it was found that one data value was incorrectly recorded as 25 instead of the correct value 35. If alpha and sqrt(beta) denote the corrected mean and standard deviation respectively, find (alpha, beta).

1. (11, 26)
2. (10.5, 25)
3. (11, 25)
4. (10.5, 26)

Correct answer: (10.5, 26)

Solution

When one entry changes from 25 to 35, the sum increases by 10, shifting the mean from 10 to 10.5. The corrected sum of squares gives a variance of 26, so sqrt(beta) = sqrt(26).

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