The problem is is that the average is presented without the range and called normal or typical. you may live your life and never experience an average day.
Most people never understand this aspect of statistics. Living in Houston, and having survived 3 out of 4 years with an above-100-year floods, I understand firsthand the clumping of events. But the "typical" guy on the street (oops, now I just violated my own rule!) has no clue what a distribution is.
Not sure how to solve this problem. Teaching statistics to everyone in not a solution (see the Monty Hall Problem [0] ).
Wow, people can be spectacularly ignorant of even simpler things like probability:
1) Scientists predicting the probability of an earthquake in a region that just had one. "If it doesn't occur, they'll say it was only a probability, and if it does, they'll claim they predicted it! Stop wasting taxpayer's money on this nonsense!"
2) "My mother chain smoked all her life and she's in her 90's. So smoking doesn't cause cancer."
