Hasty Generalization
The Fallacy
Drawing a conclusion based on a small sample size, rather than looking at statistics that are much more in line with the typical or average situation.
Why it's wrong
Making assumptions about a whole group or range of cases based on a sample that is inadequate (usually because it is atypical or too small). Stereotypes about people ('librarians are shy', 'wealthy people are snobs', etc.) are a common example of the principle underlying hasty generalization.
Example
My father smoked four packs of cigarettes a day since age fourteen and lived until age sixty-nine. Therefore, smoking really can't be that bad for you.