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Q.
If the mean of $n$ observations $x _1, x _2, \ldots \ldots x _{ n }$ is $\overline{ x }$, then the sum of deviations of observations from mean is :-
Statistics
Solution:
$\because \frac{ x _1+ x _2+\ldots+ x _{ n }}{ n }=\overline{ x } ......$(i)
$\therefore $ Req. sum $=\left( x _1-\overline{ x }\right)+\left( x _2-\overline{ x }\right)+\ldots .+\left( x _{ n }-\overline{ x }\right)$
$=\left( x _1+ x _2+\ldots+ x _{ n }\right)- n \overline{ x }$
$= n \overline{ x }- n \overline{ x }=0 $ (from eq. (i))