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In a very broad sense, statistics may be defined as the science of collecting and analyzing data. The tradition of collecting data is centuries old. In European countries, numerous government agencies started keeping records on births, deaths, and marriages about four centuries ago. However, scientific methods of analyzing such data are not old. Most of the advanced techniques of analyzing data have in fact been developed only in the twentieth century, and routine use of these techniques became possible only after the invention of modern computers.

During the last four decades, the use of advanced statistical techniques has increased exponentially. The collection and analysis of various kinds of data has become essential in the fields of agriculture, pharmaceuticals, business, medicine, engineering, manufacturing, product distribution, and by government or nongovernment agencies. In a typical field, there is often need to collect quantitative information on all elements of interest, which is usually referred to as the population. The problem, however, with collecting all conceivable values of interest on all elements is that populations are usually so large that examining each element is not feasible. For instance, suppose that we are interested in determining the breaking strength of the filament in a type of electric bulb manufactured by a particular company. Clearly, in this case, examining each and every bulb means that we have to wait until each bulb dies. Thus, it is unreasonable to collect data on all the elements of interest. In other cases, as doing so may be either quite expensive, time‐consuming, or both, we cannot examine all the elements. Thus, we always end up examining only a small portion of a population that is usually referred to as a sample. More formally, we may define population and sample as follows: