What word means the same as average?

median is a synonym of average.

Wikipedia isn't an absolute authority on terminology. I've never encountered a function called "average" which calculated the median by default, nor (admittedly) a person who referred to it as such within the scholastic circles. True, the case might be made that there are people and even groups who don't, and I personally have reasoned with teachers regarding narrow perceptions over the years, but in a multiple choice setting I'd recommend going with the expected answer.