Population vs Sample 

Population and sample are essential in statistics, as they form the foundation of data collection and analysis. A population includes all members of a specified group, whereas a sample is a smaller, manageable portion of that group used to draw conclusions. Since studying an entire population is often impractical, using samples offers a cost-effective and time-saving approach while still providing meaningful insights into the population’s behavior. This article explains the concepts of population and sample, along with their applications and examples.

Table of Contents:

• What is Population?
  • Types of Population
• What is Sample?
  • Types of Sample
  • Why Sampling Is Essential in Research?
• Ways of Collecting Data From a Population
• Key Steps Involved in the Sampling Process
• Difference Between Population and Sample
  • Visual Comparison: Population vs Sample
  • Population Parameter vs Sample Statistic
  • Population and Sample Formulas
• Real-World Examples
• Conclusion

What is Population?

In statistics, a population is the total collection of people, objects, or data to be analysed, or about which you will reach conclusions. The population can be explained as:

• Complete Group: A population is all elements that meet a set of criteria established by the study. If you are researching college students’ stress levels in the US, then your population is all college students in the US.
• Not limited to people: A population can comprise people, animals, products, events, or even observations – anything on which you are conducting a study.
• Used to Define the Scope: The population is narrowed down to where the study will be conducted. A study may or may not be able to reach conclusions about a whole population. The aim is to describe or estimate a set of characteristics, known as parameters, of a population or group.

Types of Population

1. Finite Population: Countable, such as all employees in a company.
2. Infinite Population: Theoretically uncountable, like all possible outcomes of rolling a die.
3. Real Population: Actually exists, like all the bikes produced in 2024.
4. Hypothetical Population: Based on assumptions or potential outcomes, like all results of a fair coin toss.

Statistical Parameters

• μ (Mu): The mean/average of a population
• σ (Sigma): The standard deviation of a population
• P: A proportion of a population

Challenges

• Researchers will work with a population that takes a lot of time and money, or may be impossible to accomplish. 
• Researchers will often work with a sample, or a smaller subset of the population, when making inferences.

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What is Sample?

A sample is a selection of a subset of a population that is chosen to conduct a study or analysis. Collecting data from all members of a population is not practical because of the time, expense, or availability restrictions, so researchers select a subset that represents the larger group. 

Purpose

• A sample consists of some of the members of the population. 
• For example, if your population is all high school students in the United States, your sample might comprise a thousand students from different geographic regions. 
• The primary goal of sampling is to generalise the population. 
• There will be some sort of population available for study, and we will collect data from that population in the form of a sample. 
• Researchers will analyse the sample data and apply statistical techniques to estimate characteristics for the entire population. 

Types of Sample

1. Convenience sampling: Chosen for their convenience, generally not acceptable for accuracy. 
2. Random sampling: Every person in the population has an equal chance of being chosen. 
3. Stratified sampling: The population is split into groups, and samples are taken from each group.
4. Systematic sampling: You take the samples in a set pattern (e.g., every 10th person).

Statistic Parameters

• Statistic: A value (like mean or proportion) derived from a sample. 
• Sample mean (x̄): The average value in a sample. 
• Sample proportion (p̂): The proportion of the sample that has a particular characteristic. 
• Sample standard deviation (s): Indicates how far apart observations are from each other; helps to show the spread or variability of the sample.

Advantages

• More efficient and cheaper than surveying the whole population.
• Faster decision-making with low resources.
• Makes research more manageable.

Challenges

• Poor sampling methods will lead to biased results.
• Under-represented groups and/or over-represented groups lead to misconceptions.

Why Sampling Is Essential in Research?

Sampling is the most fundamental component of any research study, especially when the population is too large to be analysed completely. Sampling is a smart, effective, and reasonable approach that researchers can take in order to make trustworthy statements, as opposed to collecting information from every person or unit.

It is a scientific requirement in most cases. It is a better and more cost-effective way to acquire information, make decisions, and draw inferences about a larger population. If done correctly, sampling allows researchers to balance the trade-offs between efficiency, accuracy, and feasibility. This makes it a vital component of any successful research approach or strategy.

Ways of Collecting Data From a Population

1. Complete Census

• Data from every unit in the population.
• High accuracy, but time-consuming and expensive.
• Good for small populations or important populations.

2. Administrative/Government Records

• Data is already collected (example: birth records, tax information).
• Reliable and updated frequently.
• Usually limited in data.

3. Direct Observation

• Directly observe all of the units in the entire population.
• Most useful when in a controlled data environment (example: classrooms).
• Time-consuming and may have observer bias.

4. Surveys of the Entire Population

• Surveys or interviews of every unit in a population.
• Good option for small populations with the best access.
• Risk of non-responses.

5. Automated Data Collection

• Data collection using sensors, software, or IoT devices.
• It will collect data continuously from the source directly.
• Requires significant infrastructure and cost.

6. Experimental Methods

• Directly test the entire population as part of the study on all members.
• Conducted in laboratories or testing new products.
• Usually limited to defined populations with limited access to study participants.

7. Web Scraping/Digital Exhaust

• Capture a user’s behavioural data when using a digital product or platform.
• The best use is within technology and e-commerce settings.
• Possible legal and privacy issues.

When Is Data Collection From a Population Preferred?

Data collection from the population would be preferable when:

1. Small Population Size: To study a group that is manageable and small.
2. High Accuracy Needed: If you need results with no sampling error.
3. Legally Required: If the law requires a survey, such as a national census.
4. Unique or Rare Populations: – Cases in which each unit of analysis provides unique and non-replaceable data.
5. Easily Accessible Population: The entire population can be contacted without difficulty.
6. Avoid Sampling Bias: Possible bias in samples could fail to represent the population.
7. Data Available in Complete or Historical Form: The survey already exists and is accessible. 

Key Steps Involved in the Sampling Process

Sampling is a systematic process to confirm that the sample you selected accurately reflects the population. The essential steps of the sampling process include:

1. Specify the Population: Clearly define who or what you want to study.
   Example: All college students in California.
2. Establish the Sampling Frame: Establish a list or source of units from which the sample will be drawn.
   Example: Enrolment records of California colleges and universities.
3. Select the Sampling Method: Select a probability sampling method (random, stratified) or a non-probability sampling method (convenience, judgemental). The method selected will impact how representative and unbiased your results will be.
4. Determine the Sample Size: Determine the number of units needed to produce reliable results. The determination will depend upon the size of the population, the margin of error, and the confidence level.
5. Select the Sample: Select the sample units using the method selected. Be sure that the selections are made by the process you have specified.
6. Collect the Data: Implement surveys, interviews, observations, or some other means of data collection for the sample group selected.
7. Analyse the Sample Data: Use statistical techniques in the analysis of the data and in drawing inferences about the overall population.
8. Evaluate the Sampling Process: Completing the sampling process includes looking for bias, errors, or inconsistencies to provide some assurance that the results are valid and reliable.

Difference Between Population and Sample

Visual Comparison: Population vs Sample

A population is shown as the complete group of individuals or items in a study. A sample is a smaller portion selected from this group. Visually, the sample is part of the population, used to represent the whole in research or analysis. This visualization helps to differentiate between population and sample.

Population Parameter vs Sample Statistic

Population and Sample Formulas

Real-World Examples

Let’s now look at how the concepts of population and sample are applied in real-world scenarios.

Population Examples

Case 1: 

• Goal: A company wants to measure the average salary of all employees.
• Population: All employees of the company.
• Reason: The company includes all of its employees. 

Case 2:

• Goal: A government health department wants to estimate the average life expectancy in a country.
• Population: All citizens of the country.
• Reason: The study uses the entire population of the country.

Sample Examples

Case 1:

• Goal: A researcher wants to examine the eating habits of university students.
• Sample: 200 students chosen from various applications (departments).
• Reason: The researcher examines only a sample of university students as a whole, not all.

Case 2:

• Goal: A polling agency wants to make predictions about election results.
• Sample: 1,000 registered voters chosen randomly from the population of registered voters.
• Reason: It is a selected group with characteristics that represent the larger voting population.

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Conclusion

Understanding the difference between a population and a sample is fundamental in statistical analysis. A population refers to the entire group under study, whereas a sample represents a smaller, manageable subset of that group. Since studying an entire population is often impractical, using a well-chosen sample offers a practical, cost-effective, and time-efficient way to draw meaningful insights that can be generalized to the larger group. Overall, the validity of a statistical study is fundamentally dependent on how well the sample represents the population. It is important to understand proper sampling methods to guarantee useful results. In this article, you have learnt about the Population and Sample in detail. 

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Population vs Sample – FAQs