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The mean and the standard deviation (s.d.) of five observations are 9 and 0, respectively. If one of these observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is ?
- 0
- 4
- 2
- 1
Correct answer: 2
Solution
sd = 0 means all five observations equal the mean 9. Raising the mean to 10 adds 5 to the total, so one value becomes 14: data are 9,9,9,9,14. Variance = (4*1 + 16)/5 = 4, so the standard deviation = sqrt(4) = 2.
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