The mean of the series x 1, x 2, ldots ., x n is overline X . If x 2 is replaced by λ, then the new mean is-

Question

The mean of the series x 1, x 2, ldots ., x n is overline X . If x 2 is replaced by λ, then the new mean is- (A) ( overline X - x 2+λ/ n ) (B) ( n overline X + x 2-λ/ n ) (C) (( n -1) overline X +λ/ n ) (D) ( n overline X - x 2+λ/ n )

Tardigrade Admin · Accepted Answer

∵ ( x 1+ x 2+ x 3+---+ x n / n )= overline x ...(i) When x2 is replaced by λ then text New Mean =( x 1+λ+ x 3+---+ x n / n ) =(( x 1+ x 2+ x 3+---+ x n )+λ- x 2/ n )=( n overline x +λ- x 2/ n ) by(i)

Q. The mean of the series $x_{1}, x_{2}, \dots ., x_{n}$ is $\overline{X}$ . If $x_{2}$ is replaced by $λ$ , then the new mean is-

$\frac{X - x _{2} + λ}{n}$

$\frac{n X + x _{2} - λ}{n}$

$\frac{( n - 1 ) X + λ}{n}$

$\frac{n X - x _{2} + λ}{n}$

$∵ \frac{x _{1} + x _{2} + x _{3} +---+ x _{n}}{n} = \overline{x}$ ...(i)
When $x_{2}$ is replaced by $λ$ then
$New Mean = \frac{x _{1} + λ + x _{3} +---+ x _{n}}{n}$
$= \frac{( x _{1} + x _{2} + x _{3} +---+ x _{n} ) + λ - x _{2}}{n} = \frac{n x + λ - x _{2}}{n}$ by(i)

Q. The mean of the series x1​,x2​,….,xn​ is X. If x2​ is replaced by λ, then the new mean is-

nX−x2​+λ​

nnX+x2​−λ​

n(n−1)X+λ​

nnX−x2​+λ​