If the median of the data 4, 7, x - 1, x - 3, 16, 25, written in ascending order, is 13, then x is equal to :

1. 13

2. 14

3. 15

4. 16

Here, n = 6, which is even.

By formula,

Median = $\dfrac{\dfrac{\text{n}}{2} \text{ th observation} + \Big(\dfrac{\text{n}}{2} + 1\Big) \text{ th observation}}{2}$

$\Rightarrow 13 = \dfrac{\dfrac{6}{2} \text{ th observation} + \Big(\dfrac{6}{2} + 1\Big) \text{ th observation}}{2} \\[1em] \Rightarrow 13 = \dfrac{3 \text{ rd observation} + \Big(3 + 1\Big) \text{ th observation}}{2} \\[1em] \Rightarrow 13 \times 2 = 3 \text{ rd observation} + 4 \text{ th observation} \\[1em]$

⇒ 26 = (x - 1) + (x - 3)

⇒ 26 = 2x - 4

⇒ 2x = 26 + 4

⇒ 2x = 30

⇒ x = $\dfrac{30}{2}$

⇒ x = 15.

Hence, Option 3 is the correct option.