Hasty generalization is a logical fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence. It commonly involves basing a broad conclusion upon the statistics of a survey of a small group that fails to sufficiently represent the whole population.^{[1]} Its opposite fallacy is called slothful induction, or denying the logical conclusion of an inductive argument (i.e. "it was just a coincidence").
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Person A travels through Town X for the first time. He sees 10 people, all of them children. Person A returns to his town and reports that there are no adult residents in Town X.
Person A and Person B walk past a pawn shop. Person A remarks that a watch in a window display looks like the one his grandfather used to wear. On the basis of this remark, Person B concludes that:
Context is also relevant; in mathematics the Pólya conjecture is true for numbers less than 906,150,257, but fails for this number. Assuming something to be true for all numbers when it has been shown for over 906 million cases would not generally be considered hasty, but in mathematics a statement remains a conjecture until it is shown to be universally true.
Hasty generalization is also the basis for racist beliefs and prejudices  a person will infer an attribute to common to all members of a group based on knowledge of a small sample size of that group. For example, the belief that a given person who is Jewish will be greedy, nitpicky, stingy misers or the belief because a person is black, (s)he will be loud, poor, and criminal.^{[2]}^{[3]}
The fallacy is also known as: fallacy of insufficient statistics, fallacy of insufficient sample, fallacy of the lonely fact, generalization from the particular, leaping to a conclusion, hasty induction, law of small numbers, unrepresentative sample, and secundum quid.
When evidence is intentionally excluded to bias the result, it is sometimes termed the fallacy of exclusion and is a form of selection bias.^{[4]}
