In 10 numbers, arranged in increasing order, the 7th number is increased by 8, how much will the median be changed ?

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

Since the 7th number is increased by 8, it has no effect on the 5th and 6th terms.

Hence, the median will not change.