After taking your first introductory course in statistics you probably agreed wholeheartedly with the following statement:
"A statistical distribution is symmetric if and only if it is not skewed."
After all, isn't that how we define "skewness"?
In fact, that statement is incorrect. There are distributions which have a skewness coefficient of zero, but are asymmetric.
Before considering some examples of this phenomenon, let's take a closer look at the meaning of "skewness" in the statistical context.