Introduction

In many investigations, it is impossible or impractical to collect data from every member of a population. Imagine trying to measure the height of every person in a country or count every tree in a forest. Instead, researchers collect data from a sample, which is a smaller group selected from the larger population.

A good sample should represent the population as accurately as possible. If the sample is chosen fairly, the results are more likely to reflect the true characteristics of the population. Understanding different sampling techniques helps researchers collect reliable data and avoid sampling bias.

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Population and Sample

A population is the entire group being studied.

Examples:

• All students in a school.
• Every tree in a forest.
• All households in a city.

A sample is a smaller group selected from the population.

Researchers analyse the sample and use the results to make conclusions about the whole population.

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Figure 1. A sample is a smaller group selected to represent the larger population.

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Why Do We Use Samples?

Sampling saves:

• Time.
• Money.
• Effort.

It also makes large investigations practical.

For example:

Instead of surveying every student in a school, researchers may randomly select 100 students.

If the sample is representative, the conclusions are likely to be reliable.

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Random Sampling

In a random sample, every member of the population has an equal chance of being selected.

Examples:

• Drawing names from a hat.
• Using a random number generator.
• Selecting random student ID numbers.

Random sampling helps reduce bias.

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Non-Random Sampling

A non-random sample is selected using methods that do not give everyone an equal chance of being chosen.

Examples include:

• Asking only nearby people.
• Choosing volunteers.
• Selecting the easiest people to reach.

Non-random samples are often quicker to collect but may not represent the population accurately.

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Figure 2. Random sampling gives every member an equal chance of selection, reducing bias.

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Common Sampling Methods

Simple Random Sampling

Every member has an equal chance of selection.

Example:

Randomly selecting student numbers from the school register.

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Systematic Sampling

Researchers select every nth member after a random starting point.

Example:

Choosing every 10th customer entering a shop.

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Stratified Sampling

The population is divided into groups (strata) with shared characteristics.

Samples are then selected from each group in proportion to their size.

Example:

Sampling students from each grade level in a school.

This often produces a more representative sample.

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Convenience Sampling

Researchers select individuals who are easiest to reach.

Example:

Surveying students who happen to be in the school cafeteria.

This method is quick but often introduces bias.

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Voluntary Response Sampling

People choose whether to participate.

Example:

An online poll where anyone can vote.

People with strong opinions are often more likely to respond, increasing the risk of bias.

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Figure 3. Different sampling methods have different strengths and weaknesses.

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Random vs Non-Random Samples

Researchers usually prefer random sampling whenever possible.

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Sampling Bias

Sampling bias occurs when the sample does not fairly represent the population.

This can lead to misleading conclusions.

Examples:

• Surveying only morning students about school transport.
• Studying exercise habits using only members of a sports club.
• Asking only adults about video game preferences.

Sampling bias reduces the reliability of the investigation.

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Figure 4. Sampling bias occurs when the selected sample does not accurately represent the population.

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Evaluating Sample Quality

A high-quality sample should be:

• Representative of the population.
• Large enough to reduce random variation.
• Selected fairly.
• Free from unnecessary bias.
• Appropriate for the research question.

Researchers should ask:

• Does the sample represent the whole population?
• Was the sample chosen fairly?
• Is the sample size sufficient?
• Could bias affect the conclusions?

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Choosing the Best Sampling Technique

Different investigations require different sampling methods.

The best method depends on the purpose of the investigation and the characteristics of the population.

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Why Sampling Matters

Good sampling allows researchers to:

• Save time and resources.
• Draw reliable conclusions.
• Reduce bias.
• Improve the accuracy of investigations.
• Make fair comparisons between groups.

Poor sampling can produce misleading results, even if the data is analysed correctly.

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Figure 5. Careful sampling improves the accuracy and reliability of statistical investigations.

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Worked Example

Question

A researcher wants to survey the opinions of students in a school with Grades 7–12.

Which sampling method is most appropriate?

Solution

Stratified sampling is the best choice.

The researcher divides students into grade levels (the strata) and randomly selects students from each grade in proportion to the size of that grade.

This ensures that all year levels are fairly represented.

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Real-World Connection

Before national elections, polling organisations survey a relatively small number of voters instead of asking every eligible citizen. To make their predictions as accurate as possible, they use carefully designed sampling methods that include people of different ages, regions, occupations, and backgrounds. If important groups are left out, the poll may not accurately represent the opinions of the entire population.

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Did You Know?

Although some opinion polls survey only 1,000–2,000 people, they can often estimate the views of millions with remarkable accuracy—provided the sample is large enough, randomly selected, and representative of the population. In statistics, how the sample is chosen is usually more important than simply making it larger.

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Key Terms

Convenience sampling – Selecting individuals who are easiest to reach.

Non-random sample – A sample in which not every member of the population has an equal chance of selection.

Population – The entire group being studied.

Random sample – A sample in which every member of the population has an equal chance of being selected.

Sample – A smaller group selected from a population for study.

Sampling bias – Bias that occurs when a sample does not fairly represent the population.

Simple random sampling – Selecting participants entirely by chance.

Stratified sampling – Dividing a population into groups and sampling proportionally from each group.

Systematic sampling – Selecting every nth member after a random starting point.

Voluntary response sampling – A sampling method in which individuals choose whether to participate.

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Key Takeaways

• A population is the entire group being studied, while a sample is a smaller group selected from that population.
• Random sampling gives every member of the population an equal chance of being selected and generally produces more representative results than non-random sampling.
• Common sampling methods include simple random, systematic, stratified, convenience, and voluntary response sampling.
• Sampling bias occurs when the sample does not accurately represent the population, leading to unreliable conclusions.
• A good sample is representative, fairly selected, large enough, and appropriate for the research question.
• Choosing the correct sampling technique improves the quality, accuracy, and reliability of statistical investigations.