7.1 Populations and Samples
7.1: Populations and Samples
7.1.1: Populations
In statistics, a population includes all members of a defined group that we are studying for data driven decisions.
Learning Objectives
Key Takeaways
Key Points
- It is often impractical to study an entire population, so we often study a sample from that population to infer information about the larger population as a whole.
- Sometimes a government wishes to try to gain information about all the people living within an area with regard to gender, race, income, and religion. This type of information gathering over a whole population is called a census.
- A subset of a population is called a sub-population.
Key Terms
- heterogeneous
- diverse in kind or nature; composed of diverse parts
- sample
- a subset of a population selected for measurement, observation, or questioning to provide statistical information about the population
Populations
When we hear the word population, we typically think of all the people living in a town, state, or country. This is one type of population. In statistics, the word takes on a slightly different meaning.
A statistical population is a set of entities from which statistical inferences are to be drawn, often based on a random sample taken from the population. For example, if we are interested in making generalizations about all crows, then the statistical population is the set of all crows that exist now, ever existed, or will exist in the future. Since in this case and many others it is impossible to observe the entire statistical population, due to time constraints, constraints of geographical accessibility, and constraints on the researcher’s resources, a researcher would instead observe a statistical sample from the population in order to attempt to learn something about the population as a whole.
Sometimes a government wishes to try to gain information about all the people living within an area with regard to gender, race, income, and religion. This type of information gathering over a whole population is called a census.
Sub-Populations
A subset of a population is called a sub-population. If different sub-populations have different properties, so that the overall population is heterogeneous, the properties and responses of the overall population can often be better understood if the population is first separated into distinct sub-populations. For instance, a particular medicine may have different effects on different sub-populations, and these effects may be obscured or dismissed if such special sub-populations are not identified and examined in isolation.
Similarly, one can often estimate parameters more accurately if one separates out sub-populations. For example, the distribution of heights among people is better modeled by considering men and women as separate sub-populations.
7.1.2: Samples
A sample is a set of data collected and/or selected from a population by a defined procedure.
Learning Objective
Differentiate between a sam