The following observations have been arranged in ascending order. If the median of the data is 13, find the value of x.

3, 6, 7, 10, x, x + 4, 19, 20, 25, 28.

Given observations in ascending order :

3, 6, 7, 10, x, x + 4, 19, 20, 25, 28

Here, n = 10 which is even.

By formula,

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

Given, median = 13

⇒ x + 2 = 13

⇒ x = 13 - 2

⇒ x = 11.

Hence, the value of x is 11.