Frequentist inference

The object of statistics is to make an inference about a population based on information contained in a sample. Populations are characterized by parameters, so many statistical investigations involve inferences about one or more parameters. The process of performing repetitions of an experiment and gathering data from it is called sampling.

The basic ideas of random sampling, presentation of data by way of density or probability functions, and a statistic as a function of the data, are assumed known. Computation of a statistic from a set of observations constitutes a reduction of the data (where there are $n$ items, say) to a single number. In the process of such reduction, some information about the population may be lost. Hopefully, the statistic used is chosen so that the information lost is not relevant to the problem. The notion of sufficiency, covered in the next section, deals with this idea.

Commonly used statistics are: sample mean, sample variance, sample median, sample range and mid-range. These are random variables with probability distributions dependent on the original distribution from which the sample was taken.