Out of 10 students, who appeared in a test, three secured less than 30 marks and 3 secured more than 75 marks. The marks secured by the remaining 4 students are 35, 48, 66 and 40. Find the median score of the whole group.

Let x1, x2, x3 be the marks less than 30.

Let y1, y2, y3 be the marks greater than 75.

The order of the marks will be:

x1, x2, x3, 35, 40, 48, 66, y1, y2, y3

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

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

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

= $\dfrac{1}{2}\Big[\text{the value of} (5)^{th} + \text{the value of} (6)^{th}\Big]$ term

= $\dfrac{1}{2}\Big[40 + 48\Big]$

= $\dfrac{1}{2}\Big[88\Big]$

= 44

Hence, the median score of the whole group is 44.