Hasty Generalization

A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. It is an example of jumping to conclusions.

Example: Notice that the number 1 is a square number; 3 is a prime number, 5 is a prime number, 7 is a prime number; 9 is a square number; 11 is a prime number, and 13 is a prime number.
From these observations, you may claim that all odd numbers are either prime or square, while in reality, 15 is an example that disproves the claim.

Expressed in more precise philosophical language, a fallacy of defective induction is a conclusion that has been made on the basis of weak premises, or one which is not justified by sufficient or unbiased evidence. Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions, yet only weakly buttress the conclusions, hence a faulty generalization is produced. The essence of this inductive fallacy lies on the overestimation of an argument based on insufficiently-large samples under an implied margin or error.