Hasty generalization is an informal fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence—essentially making a rushed conclusion without considering all of the variables. In statistics, it may involve basing broad conclusions regarding the statistics of a survey from a small sample group that fails to sufficiently represent an entire population. Its opposite fallacy is called slothful induction, or denying a reasonable conclusion of an inductive argument (e.g. "it was just a coincidence").
Hasty generalization usually shows the pattern
For example, if a person travels through a town for the first time and sees 10 people, all of them children, they may erroneously conclude that there are no adult residents in the town.
Or: A person is looking at a number line. The number 1 is a square number; 3 is a prime number, 5 is a prime number, and 7 is a prime number; 9 is a square number; 11 is a prime number, and 13 is a prime number. Therefore, the person says, all odd numbers are either prime or square. In reality, 15 is a counterexample.
The fallacy is also known as: