The Scope of Data

Data analysis may have diffrent scope. It is very desirable to collect data about all the enties (population) of our interest. It is, however, in most situations, either impossible or impractical to get to know all the entities. Thus we are forces to deal only with some (sample) of entities.

Population is the collection of all entities being investigated. It can be finite or infinite.
As mentined, it is either impossible or economically infeasible to directly study a population.

A formal representation of the population depends on its data type (see Data Types). Generally, a population is a set, P, of numbers or categories:

P ⊆	A subset of real numbers.
P ⊆	A subset of integers (whole numbers).
P = {c1,c2, ..., cN}	A collection (set) of N categories (labels, tokens, etc.).

Sample is a subset of the population (S ⊆ P). A sample captures actual data being analyzed in order to learn more about the population. A sample is a collection of categories, {c_r1,c_r2, ..., c_rn}, or numbers, {x_r1,x_r2, ..., x_rn} .

Examples:

 Travel Time Population (theoretically an infinite population):
  {Time it takes to drive from Boston to New Your City}

 Travel Time Sample (recorded by 9 randomly selected drivers) [h]:
  {3.62,3.55,3.65,3.16,3.49,3.54,3.2,4.03,3.73}

 Color Preference of WNEC Students Population (one would have to interview all the students on campus to get this population):
  {Color Preferences of All the Students ...}

 Color Preference Sample (collected from 8 randomly selected students):
  {blue,blue,green,red,green,yellow,brown,blue}