Hasty generalization is an informal fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence— essentially making a hasty 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").
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.
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“A true account of the actual is the rarest poetry, for common sense always takes a hasty and superficial view.”
—Henry David Thoreau (1817–1862)