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Question

# The mean and the standard deviation(s.d.) of five observations are 9 and 0, respectively. If one of the observation is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :

A
0
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B
1
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C
4
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D
2
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Solution

## The correct option is D 2 Since, the standard deviation before the change was 0, hence all the five observations were exactly equal to 9. Now, one observation is changed and the new mean is 10, ⇒9+9+9+9+x5=10⇒x=14∴S.D.=√(9−10)2+(9−10)2+(9−10)2+(9−10)2+(14−10)25=2

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