Actually, median == mean for IQ, and for any other thing that follows normal (Gaussian) distribution.

A weird point to make, because in the context of a measure specifically constructed to have a normal distribution (IQ), the median definitely is equal to the mean. You are right in the general sense, and wrong in this instance.

Depending on the context, any representative measure of central tendency, such as the mid-range, median, mode or geometric mean, can be called the average.