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  • If x represents the mean of n observations x_{1},x_{2}......x_{n} then value of sum_{i=l}^{n} ( x_{i}-bar{x}) is: (A) -1 (B) 0 (C) 1 (D) n-1

\text{If x represents the mean of n observations }\sum_{i=l}^{n}\left ( x_{i}-\bar{x} \right )x_{1},x_{2}......x_{n},\text{then value of}  \sum_{i=l}^{n}\left ( x_{i}-\bar{x} \right )\text{ is} 

(A) -1

(B) 0

(C) 1

(D) n-1

 

Answers (1)

Answer : B

Here we are given,

\sum_{i=l}^{n}\left ( x_{i}-\bar{x} \right )

\Rightarrow \bar{x}\text{ is the mean of all observations. }

\text {mean}=\frac{\text {sum of observations}}{\text {Number of observations}}

\bar{x}=\frac{\left ( x_{1}+x_{2}+x_{3}+......+x_{n} \right )}{n}

\Rightarrow n\bar{x}=\left ( x_{1}+x_{2}+.....+x_{n} \right )

\Rightarrow n\bar{x}=\sum_{i=1}^{n}x_{i}

\Rightarrow \sum_{i=1}^{n}x_{i}-n\bar{x}=0

\Rightarrow \sum_{i=1}^{n} \left ( x_{1}-\bar{x} \right )=0

Here the value of 

\sum_{i=1}^{n} \left ( x-\bar{x} \right )=0

Therefore option (B) is correct.

Posted by

infoexpert23

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