Question

The mean of n numbers $x_1,x_2,....xn$ is M. If $x_1$ is replaced by x', then the new mean is

• A. $M-x_1+x^{\prime }$
• B. $\frac{(n-1)M=x^{\prime }}{n}$
• C. $\frac{nM-x_1+x^{\prime }}{n}$
• D. $\frac{M-x_1+x^{\prime }}{n}$

Answer 1

The correct option is C $\frac{nM-x_1+x^{\prime }}{n}$

Given that:

$M=\frac{x_1+x_2+....+x_n}{n}$

$nM=x_1+x_2+....+x_n$

$nM-x_1=x_2+....+x_n$

When $x_1$ is replaced by $x^{\prime }$ then

Mean $=\frac{x^{\prime }+x_2+....+x_n}{n}$

Mean $=\frac{nM-x_1+x^{\prime }}{n}.$

Hence, this is the required answer.