In statistics, what is the reason that makes the average height replace the median height mathematically?

Question

In statistics, what is the reason that makes the average height replace the median height mathematically?

When i searched Google there are only average height available but not median height.

Answer 1

If you think of height as being approximately normally distributed, then the median and the mean are approximately equal.

In general, the median is a more interesting quantity when your distribution is skewed (e.g. annual income, salaries of baseball players). On the other hand, the mean is usually easier to estimate than the median, and so the former is preferred when the two quantities give more or less the same information.