There are several terms that are fundamental to the study of statistics. One such term, which is always in the background of any statistics problem, is a population. It is crucial to understand who or what comprises a statistical population.
A population consists of everything or everyone being studied in an inference procedure. Populations can be large in size, although this is not necessary. What is important is that a population includes all of what we are curious about.
To make the concept of a population clear, we will look at a few examples:
- If we want to know the mean weight of all 20 year olds in the U.S., then the population is all individuals who are 20 years old and living in the U.S.
- If we want to know the proportion of middle aged men who do not have a heart attack after taking a certain drug, then the population is the set of all middle aged men.
- If we want to determine the mean I.Q. score of all ten year olds in Canada, then the population is all ten year old who are in Canada.
Limitations With Populations
Although the population is what we wish to study, it is very rare to be able to perform a census of every individual member of the population. Due to constraints of resources it is nearly impossible to perform a measurement on every subject in a population.
Instead inferential statistics steps in. Rather than performing our measurement on every member of the population, we consider a subset of this population. This subset is called a statistical sample. Measurements of the individuals in the sample tell us about corresponding measurements in the population.
We must be careful when we identify a population. For example, the mean weight of 20 year old people in the U.S. may not be as helpful to us as knowing the mean weight of 20 year old males and of 20 year old females. Thus we have split our original population into two subpopulations by use of gender.
When we are studying a population, we should be on the lookout for potential subpopulations. Typically we obtain better results when we recognize the mixture of types of individuals in our population. Different sampling techniques, such as forming stratified samples, can help in dealing with subpopulations.