That branch of statistics which is concerned with making general statements about a group or ‘population’ of items on the basis of imperfect information about that group. For example, we may be interested in trying to know in advance who will win the next General Election. By taking a random sample of voters we may obtain information on voting intentions, but this information is imperfect since it does not describe with certainty what all the voters will in fact do. Nevertheless, it is possible to generalize about the population on the basis of the sample. The techniques of statistical inference are primarily concerned with the question of the degree of confidence which can be placed on the generalizations and the margins of error which may be involved. In this they rely heavily on methods of probability theory. It is rarely possible, especially in econornics, to obtain perfect information about the group of things under study; since it is however desirable to examine relationships, test hypotheses and make measurements for the group as a whole, techniques of statistical inference have become extremely important.
Reference: The Penguin Dictionary of Economics, 3rd edt.