Question:
The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :
The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :
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S.D. 0 means all five observations equal 9; changing one so that the mean is 10 fixes the new value.
Updated On: Nov 11, 2026
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The Correct Option is C
Solution and Explanation
S.D. = 0 means every observation equals the mean 9, so the data is 9, 9, 9, 9, 9 (sum 45).
New mean 10 gives new sum 50, so the changed observation is \(9 + 5 = 14\). New data: 9, 9, 9, 9, 14.
Deviations from the mean 10: \(-1, -1, -1, -1, +4\).
Variance \(= \frac{1+1+1+1+16}{5} = \frac{20}{5} = 4\), so s.d. \(= 2\).
Answer: (3) 2
New mean 10 gives new sum 50, so the changed observation is \(9 + 5 = 14\). New data: 9, 9, 9, 9, 14.
Deviations from the mean 10: \(-1, -1, -1, -1, +4\).
Variance \(= \frac{1+1+1+1+16}{5} = \frac{20}{5} = 4\), so s.d. \(= 2\).
Answer: (3) 2
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