Inductive reasoning refers to a variety of methods of reasoning in which the conclusion of an argument is supported not with deductive certainty, but at best with some degree of probability. Unlike deductive reasoning (such as mathematical induction), where the conclusion is certain, given the premises are correct, inductive reasoning produces conclusions that are at best probable, given the evidence provided.

The types of inductive reasoning include generalization, prediction, statistical syllogism, argument from analogy, and causal inference. There are also differences in how their results are regarded.

A generalization (more accurately, an inductive generalization) proceeds from premises about a sample to a conclusion about the population. The observation obtained from this sample is projected onto the broader population.

For example, if there are 20 balls—either black or white—in an urn: to estimate their respective numbers, a sample of four balls is drawn, three are black and one is white. An inductive generalization may be that there are 15 black and five white balls in the urn. However this is only one of 17 possibilities as to the actual number of each color of balls in the urn (the population) -- there may, of course, have been 19 black and just 1 white ball, or only 3 black balls and 17 white, or any mix in between. The probability of each possible distribution being the actual numbers of black and white balls can be estimated using techniques such as Bayesian inference, where prior assumptions about the distribution are updated with the observed sample, or maximum likelihood estimation (MLE), which identifies the distribution most likely given the observed sample.

How much the premises support the conclusion depends upon the number in the sample group, the number in the population, the degree to which the sample represents the population (which, for a static population, may be achieved by taking a random sample). The extent to which the sample represents the population depends on the reliability of the procedure used for individual observations, which is not always as simple as taking a random element from a static population, which in itself is not always simple. The greater the sample size relative to the population and the more closely the sample represents the population, the stronger the generalization is. The hasty generalization and the biased sample are generalization fallacies.

A statistical generalization is a type of inductive argument in which a conclusion about a population is inferred using a statistically representative sample. For example:

The measure is highly reliable within a well-defined margin of error provided that the selection process was genuinely random and that the numbers of items in the sample having the properties considered are large. It is readily quantifiable. Compare the preceding argument with the following. "Six of the ten people in my book club are Libertarians. Therefore, about 60% of people are Libertarians." The argument is weak because the sample is non-random and the sample size is very small.

Statistical generalizations are also called statistical projections and sample projections.