POPULATION
POPULATION
IN STATISTICS
1.
Learning Objectives
After studying this topic, the learner
should be able to:
· Define
population in statistics.
· Explain
the characteristics and types of population.
· Distinguish
target population, accessible population, and sample.
· Differentiate
population parameters from sample statistics.
· Apply
the concept to educational research situations.
· Explain
why a clearly defined population is essential for sound research conclusions.
Image 01:
2. Meaning of Population
Population in statistics refers to the
complete set of individuals, objects, events, or observations possessing
characteristics relevant to a particular study and about which the researcher
wants to draw conclusions.
In simple words, "population" means the
entire group of interest in a research study.
Examples
· All
students in a school.
· All
teachers in Kerala.
· All
M.Ed. students in a university.
· All
schools in a district.
Educational
research example
If a researcher studies the reading habits
of higher secondary students in Kerala, all higher secondary students in Kerala
constitute the population when this is the defined study population.
3.
Characteristics of a Population
Clearly
defined
The researcher should precisely specify
who or what belongs to the population, including relevant geographical,
educational, or time boundaries.
Common
characteristics
Members share characteristics relevant to
the research problem.
Finite
or infinite
A population may be limited and countable
or unlimited/theoretically infinite.
Study-specific
The population depends on the research
question and purpose of the study.
Observable
or measurable
The characteristics being studied should
be capable of observation, recording, or measurement.
4.
Types of Population
4.1
Finite Population
A finite population contains a limited and
countable number of members.
· Students
in a particular class.
· Teachers
in a particular school.
· Books
in a library.
· Students
enrolled in a university.
Example: If a school has 1,200 students,
the student population is finite because its members can be counted.
4.2
Infinite Population
An infinite population is unlimited or is
treated as unlimited for practical statistical purposes. It may be impossible
or impractical to count all possible members or observations.
· Possible
outcomes of repeated statistical experiments.
· Continuous
production measurements from an ongoing process.
· Theoretical
outcomes of repeated trials.
5.
Target Population, Accessible Population, and Sample
5.1
Target Population
The target population is the complete
group to which the researcher intends to generalize the findings.
Example: In a study on job satisfaction
among secondary school teachers in Kerala, all secondary school teachers in
Kerala may constitute the target population.
5.2
Accessible Population
The accessible population is the portion
of the target population that the researcher can realistically reach and study.
Example: From all secondary teachers in
Kerala, teachers in selected accessible districts or schools may form the
accessible population.
5.3
Sample
A sample is a selected subset of the
population from which the researcher actually collects data.
Example: If 10,000 teachers form the
population and 500 teachers are selected, 10,000 represents the population and
500 represents the sample.
Researchers use samples because studying
an entire population may be time-consuming, expensive, or practically
impossible.
Key relationship: Target Population →
Accessible Population → Sample
6.
Population vs. Sample
|
Population |
Sample |
|
Entire group |
Part of the group |
|
Usually larger |
Usually smaller |
|
Contains all members of the defined
population |
Contains selected members |
|
May be difficult or costly to study
completely |
Usually more practical to study |
|
Described by parameters |
Described by statistics |
Key relationship: Population → Parameter; Sample → Statistic.
Image 02:
A parameter is a numerical value that
describes a characteristic of the entire population.
7.1
Population Mean μ)
μ (mu) represents the population mean, or
average value of the entire population.
Example: If the average age of all
teachers in a school is 35 years, then μ = 35 years.
7.2
Population Standard Deviation (σ)
σ (sigma) represents the population
standard deviation. It indicates the spread or variability of observations
around the population mean.
7.3
Population Proportion (P)
P represents the proportion of population
members possessing a particular characteristic.
Example: If 600 of 1,000 students use a
digital learning platform, P = 600/1000 = 0.60 or 60%.
8.
Parameter and Statistic
|
Aspect |
Population |
Sample |
|
Numerical description |
Parameter |
Statistic |
|
Common symbols |
μ, σ, P |
x̄, s, p |
|
Describes |
Entire population |
Selected sample |
Memory aid: P in Population → Parameter; S in Sample →
Statistic.
9.
Population in Educational Research
Population is especially important in
educational research because studies commonly focus on students, teachers,
schools, parents, administrators, and teacher trainees.
Research topic: Study
habits of higher secondary students in Kerala
Population: All higher secondary students
in Kerala.
Research topic: Job
satisfaction among teachers in Malappuram district
Population: All teachers in the Malappuram district.
Research topic: Digital
learning practices of M.Ed. students
Population: All M.Ed. students within the
defined study setting.
10.
Importance of Population in Research
Defining the population establishes the
boundaries and purpose of the research. It helps the researcher move logically
from the research problem to sampling, data collection, analysis, and
interpretation.
Identify
who or what is being studied: Clearly identifies
the individuals, groups, objects, or events that are the focus of the research.
Decide the
appropriate sampling method: A well-defined population
helps the researcher select a sampling technique suited to the study.
Determine
the sample size: Knowledge of the
population and research design contributes to deciding an appropriate number of
participants or units.
Establish
the scope of the research: Defines the boundaries
and limits of the study, keeping the investigation focused and manageable.
Generalize
findings appropriately: Clarifies the group to
which conclusions may reasonably be extended, subject to the study design and
sampling quality.
Avoid
ambiguity in research: Make inclusion and
exclusion criteria clearer and reduce confusion about who belongs to the
study.
Improve the
validity and reliability of conclusions: A
clearly specified population and suitable sampling process support more
accurate, consistent, and trustworthy research conclusions.
11. Concept Map: Population in Statistics
Image 03:
12. Importance – Concept Map Explained
The seven points in the concept map can be
remembered as a research sequence:
1. Identify who or what
is being studied—Clearly identifies the
individuals, groups, objects, or events that are the focus of the research.
2. Decide the appropriate
sampling method—a well-defined population
helps the researcher select a sampling technique suited to the study.
3. Determine the sample size—Knowledge of the population and research
design contributes to deciding an appropriate number of participants or units.
4. Establish the scope of
the research—Defines the boundaries and limits of
the study, keeping the investigation focused and manageable.
5. Generalize findings appropriately—Clarifies the group to which
conclusions may reasonably be extended, subject to the study design and
sampling quality.
6. Avoid ambiguity in research—makes inclusion and exclusion
criteria clearer and reduces confusion about who belongs to the study.
7. Improve the validity
and reliability of conclusions—A clearly
specified population and suitable sampling process support more accurate,
consistent, and trustworthy research conclusions.
13.
Quick Revision Points
· Population
= entire group of interest.
· Sample
= selected part of the population.
· Target
population = group to which the researcher intends to generalize.
· Accessible
population = part of the target population that can actually be reached.
· Finite
population = limited and countable.
· Infinite
population = unlimited or treated as unlimited for practical purposes.
· Parameter
describes a population.
· A statistic describes a sample.
· μ
= population mean; σ = population standard deviation; P = population
proportion.
· A
clearly defined population supports appropriate sampling and meaningful
conclusions.
14.
Possible Examination Questions
1. Define "population" in
statistics and explain its characteristics.
2. Explain the types of
population with suitable examples.
3. Differentiate target
population, accessible population, and sample.
4. Distinguish population
and sample.
5. What is a population
parameter? Explain μ, σ, and P.
6. Differentiate parameter
and statistic.
7. Explain the importance of
defining population in research.
15. Reference
Kumar, R. (2019). Research Methodology: A Step-by-Step Guide for Beginners (5th ed.). SAGE Publications.
Wilson, J. H., & Joye, S. W. (2016). Research Methods and Statistics: An Integrated Approach. SAGE Publications.
Kalton, G. (2020). Introduction to Survey Sampling (2nd ed.). SAGE Publications.
Andrade, C. (2020). “Sample Size and Its Importance in Research.” Indian Journal of Psychological Medicine, 42(1), 102–103.
Statistics without tears: Populations and samples.
17. Conclusion
Population is a fundamental concept in
statistics and research. It refers to the complete group about which a
researcher seeks information or wishes to draw conclusions. A clear definition
of the population supports appropriate sampling, meaningful data collection, and
justified interpretation. Understanding the relationship among population,
sample, parameter, and statistic is therefore essential for educational
research.
“A well-defined population is the foundation of a well-designed
research study.”.
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