Populations and Samples
Learning Outcomes
- Determine whether a value calculated from a group is a statistic or a parameter
- Identify the difference between a census and a sample
- Identify the population of a study
- Determine whether a measurement is categorical or qualitative
Selecting A Focus
Before we begin gathering and analyzing data we need to characterize the population we are studying. If we want to study the amount of money spent on textbooks by a typical first-year college student, our population might be all first-year students at your college. Or it might be:- All first-year community college students in the state of Washington.
- All first-year students at public colleges and universities in the state of Washington.
- All first-year students at all colleges and universities in the state of Washington.
- All first-year students at all colleges and universities in the entire United States.
- And so on.
Population
example
A newspaper website contains a poll asking people their opinion on a recent news article. What is the population?Answer: While the target (intended) population may have been all people, the real population of the survey is readers of the website.
Parameter
Census
Sample
Statistic
example
A researcher wanted to know how citizens of Tacoma felt about a voter initiative. To study this, she goes to the Tacoma Mall and randomly selects 500 shoppers and asks them their opinion. 60% indicate they are supportive of the initiative. What is the sample and population? Is the 60% value a parameter or a statistic?Answer: The sample is the 500 shoppers questioned. The population is less clear. While the intended population of this survey was Tacoma citizens, the effective population was mall shoppers. There is no reason to assume that the 500 shoppers questioned would be representative of all Tacoma citizens. The 60% value was based on the sample, so it is a statistic.
The examples on this page are detailed in the following video. https://youtu.be/NlcDpqnqBKYTry It
To determine the average length of trout in a lake, researchers catch 20 fish and measure them. What is the sample and population in this study?Answer: The sample is the 20 fish caught. The population is all fish in the lake. The sample may be somewhat unrepresentative of the population since not all fish may be large enough to catch the bait.
Licenses & Attributions
CC licensed content, Original
- Revision and Adaptation. Provided by: Lumen Learning License: CC BY: Attribution.
CC licensed content, Shared previously
- Populations and Samples. Authored by: David Lippman. Located at: http://www.opentextbookstore.com/mathinsociety/. License: CC BY-SA: Attribution-ShareAlike.
- Populations. Authored by: Nils Dougan. License: CC BY-NC: Attribution-NonCommercial.
- Population and sample. Authored by: OCLPhase2's channel. License: CC BY: Attribution.
- Question ID 6910, 33101. Authored by: Lippman, David. License: CC BY: Attribution. License terms: IMathAS Community License CC-BY + GPL.