The following observations have been arranged in ascending order. If the median of these observations is 58, find the value of x.

24, 27, 43, 48, x - 1, x + 3, 68, 73, 80, 90.

Number of observations, n = 10 (even)

Median = $\dfrac{1}{2}\Big[\text{the value of} \Big(\dfrac{n}{2}\Big)^{th} + \text{the value of} \Big(\dfrac{n}{2} + 1\Big)^{th}\Big]$ term

⇒ 58 = $\dfrac{1}{2}\Big[\text{the value of} \Big(\dfrac{10}{2}\Big)^{th} + \text{the value of} \Big(\dfrac{10}{2} + 1\Big)^{th}\Big]$ term

⇒ 58 = $\dfrac{1}{2}\Big[\text{the value of} (5)^{th} + \text{the value of} (5 + 1)^{th}\Big]$ term

⇒ 58 = $\dfrac{1}{2}\Big[(x - 1) + (x + 3)\Big]$

⇒ 58 = $\dfrac{1}{2}\Big[x - 1 + x + 3\Big]$

⇒ 58 = $\dfrac{1}{2}\Big[2x + 2\Big]$

⇒ 58 = x + 1

⇒ x = 58 - 1

⇒ x = 57

Hence, the value of x is 57.