Question

Median of the data $\frac{x}{3},\frac{x}{6},\frac{x}{9}.\frac{x}{2},\frac{x}{8},\frac{x}{4}$ is $5$, then find the value of 'x'.

Answer 1

$\Rightarrow$ The given numbers are $\frac{x}{3},\frac{x}{6},\frac{x}{9},\frac{x}{2},\frac{x}{8},\frac{x}{4}$

$\Rightarrow$ Arranging given numbers in ascending order $\frac{x}{9},\frac{x}{8},\frac{x}{6},\frac{x}{4},\frac{x}{3},\frac{x}{2}$

$\Rightarrow$ Number of observation $\left(n\right)=6$

$\Rightarrow$ Number of observation is even number.

$\therefore$ $Median={(\frac{n}{2}+1)}^{th}observation={(\frac{6}{2}+1)}^{th}=4^{th}observation$

Here, $4^h$ observation is $\frac{x}{4}$

$\therefore$ According to the question,

$\Rightarrow$ $\frac{x}{4}=5$

$\therefore$ $x=20$