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

29, 32, 48, 50, x, x + 2, 72, 75, 87, 91.

Here n = 10, which is even.

By formula,

$\text{Median} = \dfrac{\dfrac{n}{2}\text{th observation} + \Big(\dfrac{n}{2} + 1\Big)\text{th observation}}{2} \\[1em] \therefore 63 = \dfrac{\dfrac{10}{2}\text{th observation} + \Big(\dfrac{10}{2} + 1\Big)\text{th observation}}{2} \\[1em] \Rightarrow 126 = \text{5th observation + 6th observation} \\[1em] \Rightarrow 126 = x + x + 2 \\[1em] \Rightarrow 2x = 126 - 2 \\[1em] \Rightarrow 2x = 124 \\[1em] \Rightarrow x = 62.$

Hence, the value of x = 62.