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Sampling theory is the field of statistics that is involved with the
collection, analysis and interpretation of data gathered from random
samples of a population under study. The application of sampling theory
is concerned not only with the proper selection of observations from the

population that will constitute the random sample; it also involves the
use of probability theory, along with prior knowledge about the
population parameters, to analyze the data from the random sample and

develop conclusions from the analysis. The normal distribution, along
with related probability distributions, is most heavily utilized in
developing the theoretical background for sampling theory.

A sample space that contains a finite number or a countable set
(i.e., as many elements as there are whole numbers) of sample points is a
discrete sample space. Conversely, a sample space that contains an

infinite and uncountable set of sample points, with as many elements as
there are points on a line, is a continuous sample space.
Statisticians employ different procedures in choosing the

observations that will constitute their random samples of the population.
The objective of these procedures is to select samples that will be
representative of the population from where they originate. These

samples, also known as random samples, will have the property that
each sample has the same probability of being drawn from the
population as another sample.

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