The weights (in kg) of 8 children are given below:

10.6, 12.7, 9.8, 17.2, 13.4, 15, 16.5, 14.3

Find the median weight.

By arranging data in ascending order, we get:

9.8, 10.6, 12.7, 13.4, 14.3, 15, 16.5, 17.2

Number of observations, n = 8, which is even.

By formula,

$\Rightarrow \text{Median} = \dfrac{\Big(\dfrac{\text{n}}{2}\Big) \text{th} \text{ term} + \Big(\dfrac{\text{n}}{2} + 1\Big)\text{th} \text{ term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\Big(\dfrac{8}{2}\Big) \text{th} \text{ term} + \Big(\dfrac{8}{2} + 1\Big)\text{th} \text{ term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{4\text{th} \text{ term} + (4 + 1)\text{th} \text{ term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{4\text{ th} \text{ term} + 5\text{ th} \text{ term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{13.4 + 14.3}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{27.7}{2} \\[1em] \Rightarrow \text{Median} = 13.85$

Hence, median weight = 13.85 kg.