For the following set of numbers, find the median :

10, 75, 3, 81, 17, 27, 4, 48, 12, 47, 9, 15.

On arranging the numbers in ascending order we get,

3, 4, 9, 10, 12, 15, 17, 27, 47, 48, 75, 81.

Here, n (no. of observations) = 12, which is even.

$\therefore \text{Median} = \dfrac{\dfrac{n}{2} \text{th observation} + \big(\dfrac{n}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\dfrac{12}{2} \text{th observation} + \big(\dfrac{12}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\text{ 6th observation + 7th observation}}{2} \\[1em] = \dfrac{15 + 17}{2} \\[1em] = \dfrac{32}{2} \\[1em] = 16.$

Hence, median = 16.