Following data have been arranged in the ascending order.

29, 32, 48, 50, x, x + 2, 72, 78, 84, 95.

If the median of the data is 63, the value of x is :

1. 31

2. 62

3. 124

4. 134

Here n = 10, which is even.

By formula,

$\Rightarrow \text{Median} = \dfrac{\left(\dfrac{n}{2}\right)^{\text{th}} \text{term} + \left(\dfrac{n}{2} + 1\right)^{\text{th}} \text{term}}{2} \\[1em] \Rightarrow \text{63} = \dfrac{\left(\dfrac{10}{2}\right)^{\text{th}} \text{term} + \left(\dfrac{10}{2} + 1\right)^{\text{th}} \text{term}}{2} \\[1em] \Rightarrow \text{63} = \dfrac{\text{5th term} + \text{6th term}}{2} \\[1em] \Rightarrow \text{63} = \dfrac{\text{x} + \text{x+2}}{2} \\[1em]$

⇒ 126 = 2x + 2

⇒ 2x = 124

⇒ x = 62.

Hence, option 2 is the correct option.