The median of all $4$- digit numbers that are divisible by $7$ is

Four digits number which is

divisible by $7$ are $1001,1008,1015,\dots$ $9996$

Hence, total number of such numbers
$=1286$

${\left(\frac{N}{2}\right)}^{th}$observation

Median $=\frac{+{\left(\frac{N}{2}+1\right)}^{\text{th }}\text{ observation }}{2}$

$[\because N$ is even $]$

${\left(\frac{1286}{2}\right)}^{\text{th }}$ observation

Median $=\frac{+{\left(\frac{1286}{2}+1\right)}^{\text{th }}\text{ observation }}{2}$

$=\frac{{643}^{\mathrm{th}}+{644}^{\mathrm{th}}}{2}$

$=\frac{(1001+(642\left)7\right)+\left(1001\right)+\left(643\right)7)}{2}$

$=\frac{2\left(1001\right)+7(642+643)}{2}$

$=\frac{2\left(1001\right)+7\left(1285\right)}{2}$

$=1001+4497.5=5498.5$