Contents

- Definition
- What Is Meant by a Random Sample?
- What Is Random Sampling and Why Is It Used?
- The Four Types of Random Sampling
- What Is the Difference Between Random and Non Random Sampling?
- What Are the Advantages of Random Sampling?
- What Are the Limitations of Random Sampling?
- Three Examples of Random Sample in Mathematics

# Random Sample|Definition & Meaning

## Definition

A **sample** that is chosen from a population **randomly** such that each member of the **population** has an equal **probability** of being selected is called a random sample. For example, **choosing** 2 students from a class of 20 by randomly **drawing** names from a list is a random sample.

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Figure 1 – Random Sampling

## What Is Meant by a Random Sample?

A subset of people chosen at random from a **broader** **population** has an equal **probability** of being included in the sample, which is why it is called a random sample.

This **reduces** the likelihood of selection bias and ensures that the sample **accurately** and **impartially** reflects the population. Using this, **conclusions** may be **reached** about the population from which the sample was taken.

## What Is Random Sampling and Why Is It Used?

The process of choosing a small group of people at random from a larger **population ensures** that each person has an equal **probability** of being chosen for the sample. This **reduces** the **possibility** of selection bias and **guarantees** that the sample is **representative** of the population.

Random sampling is employed in **statistics** and **research** to infer the characteristics of a population from a sample. For example, if a sample of 100 **individuals** is selected randomly from a population of 1,000, and it is found that 10% of the sample has a certain **characteristic**, it can be inferred that **approximately** 10% of the population also has that characteristic.

Random sampling is also used in quality control, survey research, and other **fields** to **estimate** population **parameters** and test **hypotheses**.

It’s important to note that random sampling is just one of many **sampling techniques**, and it’s not always the best choice for every research or **experimentation** design. In some **cases**, other sampling methods, such as **stratified**, cluster, or systematic sampling, might be more appropriate.

Figure 2 – Systematic Random Group

## The Four Types of Random Sampling

There are several types of random sampling techniques, but four of the most commonly used are:

**Simple Random Sampling:**In this method, individuals are chosen at random from the population without**any bias**. Every member of the population, therefore, has an equal**chance**of being**picked**as the sample.**Systematic Sampling:**With this approach, people are randomly**chosen**from the population at**regular****intervals**, like every tenth person. When the population is presented in an organized list, like a phone book or a list of workers, this**approach**is**helpful**.**Stratified Sampling:**With this technique, strata or**subgroups**of the population are created, and random samples are**drawn**from each one. When the population is diverse, and it’s**vital**to make sure that**various**subgroups are represented in the sample, this**strategy**can be helpful.**Cluster Sampling:**This technique involves grouping the population into clusters and then randomly choosing samples from each cluster. When the population is huge and**distributed**, and it is**neither****practical**nor cost-**effective**to poll every person, this strategy is helpful.

It’s crucial to remember that there are **several** other random sampling **techniques**, each of which has **pros** and **cons depending** on the research design and characteristics of the population being **investigated**.

Figure 3 – Random vs. Non-Random

## What Is the Difference Between Random and Non Random Sampling?

Random sampling and non-random sampling are two different methods of selecting a sample from a population.

In order to provide every person in the population an equal chance of being included in the sample, random sampling is a technique used to choose a small group of people from a **larger population**.

This reduces the **likelihood** of selection bias and **ensures** that the sample is representative of the population.

On the other hand,** non-random** sampling is a technique for choosing a sample in which the people are not picked at random. Instead, the sample is chosen using some bias or **criterion**, such as **voluntarism**, **convenience**, or **opinion**.

This method can **introduce** bias and lead to a sample that is not representative of the population.

It’s important to note that non-random sampling is not always bad or invalid; it all **depends** on the research **goals** and what the sample will be **used** for.

For instance, a researcher could utilize non-random sampling techniques like convenience sampling if they wish to** examine a particular** segment of the population, such as** illness patients**. However, random sampling is **typically** **favored** if the **objective** is to draw conclusions about the population as a whole.

## What Are the Advantages of Random Sampling?

Random sampling is a **widely** used method for selecting a sample that is representative of a population. The following are some of the **principal** benefits of random sampling:

**Representativeness:**In order to**ensure**that the sample is representative of the population, random sampling makes sure that**every member**of the population has an equal chance of being**included**in it.**Generalization:**Random sampling allows for the generalization of the findings to the population at large, which means that the**results obtained**from the sample can be applied to the e**ntire population.****Estimation and Hypothesis Testing:**Random sampling allows researchers to estimate population**parameters**and test**hypotheses**, which can be useful for making**inferen****ces**about the population.**Reduction of Bias:**Random sampling**reduces**the chance of the researcher’s own biases**influencing**the sample selection.**Ease of implementation:**Random sampling is relatively easy to**implement**and**understand**, making it accessible to a wide range of researchers.**Well-established method:**Random sampling is a widely**accepted**method for selecting a sample that is representative of a population, it has been used in many research fields, and its results are easy to**interpret**.

## What Are the Limitations of Random Sampling?

Random sampling is a **widely** used and accepted method for selecting a sample that is representative of a population, but it does have some **limitations**. Some of the limitations of random sampling include the following:

**Sampling error:**Even with random sampling, there is still a chance that the sample selected may not be**perfectly**representative of the population. This can lead to**sampling error**, which is the difference between the sample statistics and the true**population parameters.****Cost:**Random sampling can be costly,**especially**when the population is large or**widely**dispersed. It can be**difficult**and expensive to obtain a representative sample when the population is hard to access.**Limited sample size:**Depending on the size of the population and the desired level of precision, the sample size required for random sampling can be large. This can be a limitation when resources and time are limited.**Nonresponse bias:**In some cases, individuals who are selected for the sample may not respond or may not be able to**respond**. This can introduce bias into the sample if the non-responders are**systematically**different from the**responders**.**Hidden population:**Sometimes, a population is**hidden**and hard to**identify**, making it**difficult**to obtain a random**sample**. For example, if trying to study a specific**disease**in a population, it may be hard to identify all the individuals with the disease.

It’s important to note that despite these **limitations**, random sampling is still **considered** a **valid** and **reliable** method for selecting a sample that is **representative** of a population, **especially** when used in **combination** with other **techniques** such as **weighting**.

## Three Examples of Random Sample in Mathematics

### Example 1

What is the average score on a math test for students in a certain school?

### Solution

A random sample of 100 students from the school can be selected, and their **test score**s can be recorded and analyzed to **estimate** the average test score of all students in the school.

### Example 2

What is the** standard deviation** of a certain set of data?

### Solution

A random sample of 100 data points from the set can be selected, and the standard deviation can be calculated for the sample data. This can be used as an **estimate of the standard** **deviation** for the **entire set of data**.

### Example 3

What is the **probability** that a certain coin is **fair**?

### Solution

A random sample of 1000 flips of the coin can be **conducted**, and the number of heads and tails can be **recorded**. The **proportion** of heads and tails in the sample can be used to **estimate** the **probability** of heads for the entire population of **coin** **flips**, **assuming** that the coin is fair.

*All images were created with GeoGebra.*