The weights (in $\mathrm{kg}$) of $8$ children are $13.4, 10.6, 12.7, 17.2, 14.3, 15, 16.5, 9.8$ and the median weight is $x \mathrm{kg}$. Find the value of $x$.

Find the median of the data $46,41,77,58,35,64,87,92,33,55,90$

In the above data, if $41$ and $55$ are replaced by $61$ and $75$ respectively, what will be the new median?

Determine the mode of the following values of a variable. 

$23, 15, 25, 40, 27, 25, 22, 25, 20$.

What is the mode of the following sizes of shoes sold by a shop on a particular day.

$5, 9, 8, 6, 9, 4, 3, 9, 1, 6, 3, 9, 7, 1, 2, 5, 9$.