Our friend, an OB/GYN, mentioned how hard her work is, because "the average baby is born at 3am."
We laughed, but then my brother asked, "What does 'average' mean when you have a 24-hour clock? It must mean the modal time or something like that."
I contributed that this is an issue in defining average wind directions, as well. The basic problem is that if you record times on a 0-24 hour scale, or wind directions on a 0-360 degree scale, and then naively average the numbers, you get meaningless results (for example, 180 degrees if the wind steadily rotates through every point of the compass).
A quick glance at our doctor friend showed she had checked out of the conversation entirely. Possibly she just felt slighted that we were not bowing down in awe at the terrible hours she keeps. But my main impression was that she lives in a world where one receives a piece of information, notes it, and stores it away. And when repeating that received information, one's listeners duly note and store it away.
Chasing down the source of the information, calling it into question, relating it to other things in the world-- these just weren't things she seemed to find pleasurable.