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If barx represents the mean of n observa...

If `barx` represents the mean of n observations `x_(1), x_(2),………., x_(n)`, then values of `Sigma_(i=1)^(n) (x_(i)-barx)`

A

`-1`

B

0

C

1

D

`n-1`

Text Solution

Verified by Experts

The correct Answer is:
B
Given, `barx= (underset(i=1)overset(n)Sigmax_(i))/n rArr underset(i=1)overset(n)Sigmax_(i)=nbarx`…………(i)
Now, `underset(i=1)overset(n)Sigma(x_(i)-barx) = underset(i=1)overset(n)Sigmax_(i)-underset(i=1)overset(n)Sigmabarx`
`=nbarx- barx underset(i=1)overset(n)Sigma1` (From Eq. (i))
`nbarx-barx.n` `[therefore underset(i=1)overset(n)Sigma(1)=n]`
=0
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