Population is a group consisting all the elements to be investigated. All the students of a university is an example of population. In general, these elements have some common points, but they have something different. The number of element `N` of a population may be a few or numerous, but statistics is used mainly to study populations with a lot of elements. Small populations have only low interest.

In many cases, we cannot study all the elements of population, so we take out a sample. Sample consists of elements chosen from a population. These elements are selected to analyze. Hence we can consider a sample as a subset of a population. Fig. 1 illustrates the relationship between population and sample.

Fig. 1 Population and Sample

The number of element `n` of a sample is defined as sample size. In many engineering applications, a sample is considered as large when `n>=30`.

The elements of a sample can be chosen from population by random or by a particular method. So, from one population, we can constitute many samples.

 

Parameter is a numerical value used to characterized a population. For example, the average revenue of a people in a country is a parameter.

On the other hand, statistic is a numerical value calculated from a sample.

In order to distinguish these concepts, we add "population" or "sample" before the name of the value. For example: population variance, sample mean.

In general, we would like to have information of population (parameter); but the collection of information for a whole population requires a lot of resources and sometimes impossible to realize. So we usually collect information from sample extracted from population, then calculate appropriate value (statistic).

The number of element of sample is less or much less than that of population, so we need highly confident methods to collect data and analyze information.