# The average of  n numbers $x_{1}, x_{2}, x_{3},.......x_{n} is M.$ If $x_{n}\: is\:$ replaced by $x^{1}$ then new average is  Option 1) $M-X_{n}+x^{1}$ Option 2) $\frac{nM-x_{n}+x^{1}}{n}$ Option 3) $\frac{(n-1)M+x^{1}}{n}$ Option 4) $\frac{M-x_{n+x^{1}}}{n}$

As we discussed in concept

ARITHMETIC Mean -

For the values x1, x2, ....xn of the variant x the arithmetic mean is given by

$\dpi{100} \bar{x}= \frac{x_{1}+x_{2}+x_{3}+\cdots +x_{n}}{n}$

in case of discrete data.

-

$M\:=\:\frac{x_{1}+x_{2}+x_{3}...x_{n}}{n}$

=> $x_{4}+x_{2}+x_{3}+\:-----\:+x_{n}\:=\:Mn$

Now $x_{4}+x_{2}+x_{3}+-------x^{1}\:=\:Mn-x_{n}+x^{1}$

New Average:

$\frac{x_{1}+x_{2}+x_{3}+-------x^{1}}{n}\:=\:\frac{Mn-x_{n}+x^{1}}{n}$

Option 1)

$M-X_{n}+x^{1}$

This option is incorrect.

Option 2)

$\frac{nM-x_{n}+x^{1}}{n}$

This option is correct.

Option 3)

$\frac{(n-1)M+x^{1}}{n}$

This option is incorrect.

Option 4)

$\frac{M-x_{n+x^{1}}}{n}$

This option is incorrect.

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