Finding minima of function.

Question

For what value of 'k' (in terms of $X_{i}$'s) following  functions will attain their minimum value $\rightarrow$ 

1. $F_{1}(k)$ = $\sum_{i=0}^{n} \left | X_{i} - k \right |$
2. $F_{2}(k)$ = $\sum_{i=0}^{n}\left ( X_{i} - k \right )^{2}$

If possible, please provide some valid proof for supporting your answer ?