Expectation value of the median of five dice roll

Question

The question goes as:

1. First of all, imagine you roll a dice five times, what is the expected median of the roll?

(the answer should be 7/2 which is exactly the same as a single roll. Found people on the internet are talking about symmetry argument, but I don't quite understand why that works)

2. Again, we roll a dice five times, calculate the expected value of the square of medium value.