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If the sum of the deviations of 50 obser...

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is

A

50

B

30

C

51

D

31

Text Solution

Verified by Experts

The correct Answer is:
D
Let the 50 observations are `x_(1),x_(2),x_(3), ..., x_(50).`
Now, deviations of these observations from 30 are
`(x_(1)-30),(x_(2)-30), (x_(3)-30), ..., (x_(50)-30)`
`because sum_(i=1)^(50)(x_(i)-30)=50 " "` (given)
`rArr sum_(i=1)^(50)x_(i)-(30xx50)=50`
`rArr sum_(i=1)^(50)x_(i)-50(30+1)=50xx31`
`therefore` mean of 50 observations `=(bar(x))=(sum_(i=1)^(50)x_(i))/(50)=31`
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