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population, the statistician is often interested in arriving at conclusions
involving the entirety of the population.
A sample is a subset of a population. In the process of data
gathering, it is often impossible or impractical to obtain the entire set of

observations for the given population. Often, a sample of the population
is taken, data collected from it, and inferences about the population are
made based on the analysis of the sample data.

Data collected from a sample that is not representative of the
population will often result in inferences that consistently overestimate
or underestimate some population characteristic; these are called biased
samples. On the contrary, unbiased samples are statistically similar to

their parent population, and inferences on a population based on

unbiased samples are more reliable than those based on biased samples.
A random sample of n observations is a sample with n

observations, selected in such a way that every such sample of the
population has the same probability of being selected. These samples are
considered to be unbiased. The field of sampling theory deals with the

process of selecting random samples, collecting data from these
samples, and analyzing it to develop inferences about the population as a
whole.

The statistician is often faced with the task of summarizing large
amounts of data in a compact format that yields meaningful information
concerning the data. Without displaying the values for each observation
taken from the population, it is possible to present the data concisely and

meaningfully using certain procedures. Such procedures often involve
frequency distributions or graphs of the data.
Statisticians utilize various kinds of measurements based on the

collected data as an initial step towards developing inferences on the
population from which observations were taken. Some measures reflect,
in a sense, the center or middle point of a set of data; others provide a

measure of the variability of the data. These measures can apply to
either the population as a whole or to a sample taken from the
population.

A statistical experiment is a process that generates a set of data.
Such a process will lead to one of a myriad of results or outcomes, each
with some possibility of occurring. The set of all possible outcomes of a
statistical experiment is called the sample space; it is denoted by S. Each

of the possible outcomes of the statistical experiment are elements of the
sample space and are called sample points.

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