Why do some plots use means, medians, and modes?

Means (averages) work great for scales that are numeric and continuous (such as temperatures).

Medians work great for scales that are numeric but have an upper limit (such as ceilings).  Ceilings are usually only reported up to 12,000 feet of altitude.  Further, what number should be used when there is no ceiling?  For these reasons, ceiling data cannot be averaged, since this upper limit would skew the resultant data.

Modes work great for scales that are cyclic or do not have an obvious middle (such as wind direction).  If prevailing winds at an airport come directly from the north, but sometimes from the east, it would not be accurate to summarize these facts with a northeast direction.