Inferential statistics is involved with complex, quantiative and mathematical procedures, as well as statistical tests of significance. It utilizes probabilistic approaches to examine sample information gathered from a specific population that we already know well, to better understand information about the population which we do not already understand well. Hence, it is about making predictions involving population values that are obscure, unknown, or unclear. It is necessary to use a 'sample' of a population as it would be impractical to look at the whole population. As we infer information about the population from the sample, this type of statistical methodology is called inferential.
It is possible to state that the two most important concepts ingrained within inferential statistics are population and probability.
A population in statistics refers to the entire group of persons, events, or things, that have at least one characteristic in common. For example, all people living in Montana. So, only the people living in within the state borders of Montana are considered part of the population. A population can be further defined by, for instance, researching all people who live in Montana, over 45 years old, have two children, and have purchased a car within the last 12 months. Hence, a population is really arbitary since the researcher can decide what common trait(s) define the population.