The following observations have been arranged in ascending order. If the median of the data is 47.5, find the value of x.

17, 21, 23, 29, 39, 40, x, 50, 51, 54, 59, 67, 91, 93.

Given data,

17, 21, 23, 29, 39, 40, x, 50, 51, 54, 59, 67, 91, 93.

Here, n = 14 which is even.

By formula,

$\text{Median} = \dfrac{\dfrac{n}{2}\text{ th observation} + \Big(\dfrac{n}{2} + 1\Big) \text{ th observation}}{2} \\[1em] = \dfrac{\dfrac{14}{2}\text{ th observation} + \Big(\dfrac{14}{2} + 1\Big)\text{ th observation}}{2} \\[1em] = \dfrac{7 \text{ th observation} + 8\text{ th observation}}{2} \\[1em] = \dfrac{x + 50}{2}.$

Given, median = 47.5

⇒ $\dfrac{x + 50}{2}$ = 47.5

⇒ x + 50 = 95

⇒ x = 95 - 50

⇒ x = 45.

Hence, the value of x is 45.