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 $=\frac{(\frac{1286}{2}{)}^{th}\text{observation}+(\frac{1286}{2}+1{)}^{th}\text{observation}}{2}$
$=\frac{643^{th}+644^{th}}{2}$
$=\frac{(1001+(642)7)+(1001)+(643)7)}{2}$
$=\frac{2(1001)+7(642+643)}{2}$
$=\frac{2(1001)+7(1285)}{2}$
$=1001+4497.5=5498.5$