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 +

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

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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 $nM = x_1 + x_2 + x_3 + ... + x_n$.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 $\frac{nM - x_n + x'}{n}$.

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

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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