The following data have been arranged in ascending order. If their median is 63, find the value of x.

34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.

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

⇒ 63 = $\dfrac{1}{2}\Big[\text{the value of} \Big(\dfrac{10}{2}\Big)^{th} + \text{the value of} \Big(\dfrac{10}{2} + 1\Big)^{th}\Big]$ term

⇒ 63 = $\dfrac{1}{2}\Big[\text{the value of} (5)^{th} + \text{the value of} (5 + 1)^{th}\Big]$ term

⇒ 63 = $\dfrac{1}{2}\Big[x + x + 2\Big]$

⇒ 63 = $\dfrac{1}{2}\Big[2x + 2\Big]$

⇒ 63 = x + 1

⇒ x = 63 - 1

⇒ x = 62

Hence, the value of x = 62.