The median of the following numbers, arranged in ascending order, is 25. Find x :

11, 13, 15, 19, x + 2, x + 4, 30, 35, 39, 46.

Here, n (no. of observations) = 10, which is even.

$\therefore \text{Median} = \dfrac{\dfrac{n}{2} \text{th observation} + \big(\dfrac{n}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\dfrac{10}{2} \text{th observation} + \big(\dfrac{10}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\text{ 5th observation + 6th observation}}{2} \\[1em] = \dfrac{x + 2 + x + 4}{2} \\[1em] = \dfrac{2x + 6}{2} \\[1em] = x + 3.$

Given, median = 25.

∴ x + 3 = 25
⇒ x = 22.

Hence, the value of x = 22.