Medium is a format for communicating or presenting information. It can also be described as the means or channel by which an aim is achieved.
"To boost sales, have you tried the Internet advertising medium?"
Median is the quantity or value at the midpoint of a set of values, such that the variable is likely to fall above or below it. It means the middle and center.
"Find the median of the following set of numbers: 12, 65, 43, 19 and 47."
You will most often see ‘medium’ used as an adjective, meaning about halfway between two extremes. For example, in clothing sizes, medium is between small and large. A person who is not particularly short or tall might be described as being of medium height.
Median, however, is a more specific term that means the middle of a series of numbers. For example, the median number of the series 56, 63, 77, 86, and 94 is 77 – 77 is hallway between 55 and 94. Sometimes people use median as a synonym for average, but it’s not truly the same.