Question

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

• A. 5797
• B. 5498.5
• C. 5499.5
• D. 5490

Answer 1

Answer: (B)

Four digits number which is divisible by $7$ are $1001, 1008, 1015, ....,9996$.
Hence, total number of such numbers $= 1286$
Median $ =\frac{(\frac{N}{2})^{th} {\text{observation}} + (\frac{N}{2} + 1)^{th} \text{observation}}{2}$
$[\because N $ is even ]
Median $ = \frac{(\frac{1286}{2})^{th} \text{observation} + (\frac{1286}{2} + 1 )^{th} \text{observation}}{2}$
$= \frac{643^{th} + 644^{th}}{2}$
$ = \frac{(1001 + ( 642)7) + (1001) + (643)7)}{2}$
$ = \frac{2(1001) + 7 (642 + 643)}{2}$
$= \frac{2(1001) + 7(1285)}{2}$
$= 1001 + 4497.5 = 5498.5$