Median means having a value that is in the middle of a series of values arranged from the smallest to the largest: “The median rate of hotels for a night in this area is around one thousand.”
Medium has the following meanings:-
1. Occupying the middle position relative to others: “At least a medium sized studio to shoot indoor scenes is an essential requirement for every TV station.”
2. A substance by which something is conveyed: “Picture of a small girl in tears, painted on the t-shirts, acted as medium to stop female feticide.”
3. An individual through whom messages are passed to and from the dead to those living and the other way, too: “The priest claimed to have the power to act as medium between the dead and the living to converse.”