The weights (in kg) of 8 children are:

Arranging the weights (in kg) in ascending order, we have:
9.8, 10.6, 12.7, 13.4, 14.3, 15, 16.5, 17.2
Here, n is 8, which is an even number.
Thus, we have

Median $=$ Mean of $\left(\frac{n}{2}\right)$ th & $\left(\frac{n}{2}+1\right)$ th observations

Median weight $=$ Mean of $\left(\frac{8}{2}\right)$ th & $\left(\frac{8}{2}+1\right)$ th observations

$=$ Mean of 4 th & 5 th observations

$=\frac{1}{2}(13.4+14.3)$

$=13.85$

Hence, the median weight is 13.85 kg.