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

Question

The median of all 4 - digit numbers that are divisible by 7 is, 5797, 5498 . 5, 5499 . 5, 5490

MARKS App · Accepted Answer

Four digits number which is

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

Hence, total number of such numbers

$= 1286$

${(\frac{N}{2})}^{t h}$ observation

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

$[∵ N$ is even $]$

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

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

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

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

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

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

$= 1001 + 4497.5 = 5498.5$