Question

If $y=f\left(x\right)$ be a monotonically increasing or decreasing function of $x$ and $M$ is the median of variable $x$, then the median of $y$ is

• A. $f\left(M\right)$
• B. $M/2$
• C. $f^{-1}\left(M\right)$
• D. none of these

Answer 1

Answer: (A)

$f\left(M\right)$

If we arrange the values $(x_1,y_1),(x_2,y_2)..(x_n,y_n)$ in asscending orders, such that $x_1<x_2<x_3<...x_n$,
Then if x=M indicates the median of 'X', such that
$x_1<x_2<x_3<M<...x_n$
Then the median of Y will be $f\left(M\right)$.