
Statistics (Greek, â€˜reckoningâ€™), in mathematics and elsewhere, is the study of the application of probability to real world situations. The difference between pure and applied mathematics is easily seen in the difference between probability and statistics. In probability, one of the most important results is the â€˜law of large numbersâ€™, which states that in a large number of experiments, the proportion of successes approaches the probability of success. In the theoretical study of probability, that result is satisfactory, since all the experiments carried out are purely theoretical, so that as many as needed can be carried out. However, statisticians are interested in knowing such information as how many experiments would be needed before the probability can be established with a certain accuracy, because their work is aimed at practicable studies of real world phenomena. (This particular interest has led to the development of statistical confidence.)
Statistics influences most, if not all, of modern society. No new products are put on the market today without a great amount of research into the market and the statistical question of whether people would buy at particular prices; no politician stands for election without statistical analysis of the trends in voting intention and the perceived importance of various issues; no insurance premium is set without statistical analysis of the risks involved; no roads are built without statistical analysis of the probable flow of traffic.
As well as its effects on society, statistics is also used to probe the most fundamental structure of the universe. Quantum mechanics uses statistical determinations of the positions of particles (that is, the ability to say that a particle is in a particular area with a certain probability) rather than the exactly defined analytical positions of earlier mechanics. The universe does not seem to be exactly determinable; and the death of determinism at the hands of modern physics is dependent on the use of statistics by its theoreticians. SMcL
Further reading D. Huff, How To Lie With Statistics. 
