Population

Definition

In statistics, the term “population” refers to the complete set of elements (people, objects, events, etc.) that share at least one common trait or characteristic. It is from this population that researchers draw samples to conduct analyses and make inferences. The term is widely used in various fields such as demography, sociology, economics, and health sciences.

Examples

National Census: A government’s collection of information about its citizens to understand demographics, such as the total population, age distribution, employment status, etc.
Customer Base: All individuals who purchase a company’s goods or services.
Clinical Trial Participants: The total group of individuals participating in a clinical study to test the effectiveness of a new drug.

Frequently Asked Questions (FAQs)

1. What is the difference between a population and a sample?

A population includes all members from a specified group, while a sample consists of a subset of the population selected for analysis.

2. Why is sampling often necessary?

Sampling is necessary because it is often impractical or impossible to collect data from every member of a population due to time, cost, or logistical constraints.

3. Can populations be infinite?

Yes, populations can be theoretically infinite when the number of possible observations is limitless, such as all possible outcomes of repeated dice rolls.

4. What is a stratified population?

A stratified population is divided into subgroups (strata) that share similar characteristics. This division facilitates more precise analyses.

5. How do researchers ensure a sample is representative of the population?

Researchers use various sampling techniques such as random sampling, stratified sampling, and systematic sampling to ensure the sample adequately reflects the larger population.

Sample: A subset of the population selected for study.
Census: A complete enumeration of a population.
Parameter: A measurable attribute that describes a characteristic of a population.
Statistic: A measure that describes an attribute of a sample.
Stratification: Division of a population into subgroups.

Online References

Suggested Books for Further Studies

“Introductory Statistics” by Sheldon M. Ross
“The Essentials of Statistics: A Tool for Social Research” by Joseph F. Healey
“Statistical Inference” by George Casella and Roger L. Berger

Fundamentals of Population: Statistics Basics Quiz

### What term is used to describe a complete enumeration of a population? - [ ] Sample - [ ] Parameter - [x] Census - [ ] Statistic > **Explanation:** A census is a complete enumeration of a population, where data is collected from every member. ### What is a significant characteristic of the population? - [ ] It consists of a limited number of elements. - [x] It includes all members from a specified group. - [ ] It is always smaller than a sample. - [ ] It excludes common traits. > **Explanation:** A population includes all members from a specified group sharing at least one common characteristic. ### Which method is often used when it is impractical to study the entire population? - [ ] Census - [x] Sampling - [ ] Data mining - [ ] Estimation > **Explanation:** Sampling is used when it's impractical to collect data from every member of the population. ### When is a population referred to as 'infinite'? - [x] When the number of possible observations is limitless. - [ ] When a population includes a finite number of elements. - [ ] When none of the members share common traits. - [ ] When it is divided into subgroups. > **Explanation:** A population is infinite when the number of possible observations is unlimited, such as repeatable dice rolls. ### What is the main goal of using sampling in statistics? - [ ] To avoid data collection. - [x] To analyze a smaller yet representative group. - [ ] To ignore the larger population's behavior. - [ ] To define the complete set of data solely. > **Explanation:** The goal of sampling is to analyze a representative subset of the population to make inferences about the entire population. ### What differentiates a sample from a population? - [ ] A sample includes every individual from a group. - [x] A sample is a subset of a population. - [ ] The terms are interchangeable. - [ ] A sample typically includes infinite observations. > **Explanation:** A sample is a smaller group selected from the population for study, differentiating it from the larger population. ### What is the role of 'parameter' in the context of population? - [ ] It is a measure of a sample. - [ ] It refers to individual data points. - [x] It describes a population characteristic. - [ ] It is the median value. > **Explanation:** A parameter is a measurable attribute that describes a characteristic of a population. ### How can researchers ensure the representativeness of a sample? - [x] By using random and systematic sampling. - [ ] By only selecting familiar elements. - [ ] By ignoring the diversity within the population. - [ ] By evaluating every member manually. > **Explanation:** Using random and systematic sampling techniques ensures that the sample accurately reflects the larger population. ### What is stratification in relation to population? - [ ] Combining unrelated samples. - [ ] Eliminating sample subgroups. - [ ] Ignoring population characteristics. - [x] Division of the population into subgroups with shared traits. > **Explanation:** Stratification involves dividing a population into subgroups that share certain characteristics to facilitate more precise analyses. ### Why might a population be divided into subgroups (strata)? - [ ] To simplify data collection. - [x] To improve the precision of analysis. - [ ] To reduce the sample size. - [ ] To decrease the study's duration. > **Explanation:** Dividing a population into strata improves the precision of analysis by ensuring that subgroups with shared characteristics are separately examined.

Thank you for advancing your understanding of statistical populations! Keep delving into the intricacies of statistical analysis to strengthen your expertise.