This is a worthy posting, particularly as so much becomes iterative statistics in "A.I." clothing. The two old (slightly hackneyed) counter-examples which are popular in lectures about measures of the central tendency are:

- One is trying to get a sense of the common sort of income in a room and then Bill Gates wanders in. Suddenly the average income becomes an amount which no one experiences.

- What is the average number of testicles in the human population? That computed central tendency is quite rare.