The average of n numbers x_1, x_2, x_3, ..., | vedclass

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(B) The initial average $M$ is given by $M = \frac{x_1 + x_2 + x_3 + ... + x_n}{n}$.This implies the sum of the $n$ numbers is $nM = x_1 + x_2 + x_3 +

Vedclass · Accepted Answer

$\frac{nM - x_n + x'}{n}$

Vedclass · Answer

(B) The initial average $M$ is given by $M = \frac{x_1 + x_2 + x_3 + ... + x_n}{n}$.This implies the sum of the $n$ numbers is $nM = x_1 + x_2 + x_3 + ... + x_n$.When $x_n$ is replaced by $x'$,the new sum of the numbers becomes $S' = (x_1 + x_2 + x_3 + ... + x_{n-1} + x_n) - x_n + x'$.Substituting the sum $nM$ for the original numbers,we get $S' = nM - x_n + x'$.The new average is the new sum divided by $n$,which is $\frac{nM - x_n + x'}{n}$.

$x_i$	$5$	$15$	$25$	$35$	$45$	$55$
$f_i$	$12$	$18$	$27$	$20$	$17$	$6$

$x_i$	$3$	$6$	$9$	$12$
$f_i$	$1$	$2$	$3$	$4$

Height (in $cm$)	$160$	$150$	$152$	$161$	$156$	$154$	$155$
No of students	$12$	$8$	$4$	$4$	$3$	$3$	$7$

The average of $n$ numbers $x_1, x_2, x_3, ..., x_n$ is $M$. If $x_n$ is replaced by $x'$,then the new average is:

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