## Types of Random Sampling

There are three types of random sampling: simple random sampling, systematic sampling, and stratified sampling.

In simple random sampling, every element in the population has an equal chance of being selected. This type of sampling is often used when the population is small.

Systematic sampling involves selecting every kth element in the population. This type of sampling is often used when the population is large.

Stratified sampling involves dividing the population into strata and selecting a sample from each stratum. This type of sampling is often used when the population is heterogeneous.

## 1. Simple Random Sampling

A simple random sample is a type of random sampling where each member of the population has an equal chance of being chosen. This type of sampling is often used when the population is small and the researcher wants to ensure that every member of the population has an equal chance of being included in the study.

## 2. Stratified Random Sampling

Stratified random sampling is a type of probability sampling that divides the population into strata and selects a sample from each stratum so that the strata are represented in the sample in the same proportions as they occur in the population. This type of sampling is used when the researcher wants to ensure that the sample is representative of the population in terms of important characteristics that are stratified (divided) into groups.

## 3. Cluster Sampling

Cluster sampling is a type of probability sampling technique where the population is divided into clusters and a sample is drawn from each cluster.

This type of sampling is often used when the population is difficult to access or when it is not possible to randomly select individuals from the population.

Cluster sampling is often used in market research and polling.

## 4. Multi-stage Sampling

Multi-stage sampling is a technique that can be used to improve the accuracy of a survey. It is a way of reducing the amount of bias in a survey by using a series of smaller samples instead of one large one. This technique is often used when the population is difficult to access or when there is not enough time or money to survey the entire population.

Multi-stage sampling involves sampling a population in a series of stages. In each stage, a smaller sample is selected from the larger population. This smaller sample is then used to select a new, smaller sample. This process is repeated until a sample that is representative of the entire population is obtained.

Multi-stage sampling is a more expensive and time-consuming technique than simple random sampling, but it can produce a more accurate survey.

## The Formula of Random Sampling

The formula of random sampling is:

x = (n * r) / (n + r)

Where:

x = the random variable

n = the population size

r = the number of samples desired

## Example of Random Sampling

To randomly sample a population, we can use a random number generator to create a list of numbers. We can then use these numbers to select individuals from the population.

For example, consider the following population:

1, 2, 3, 4, 5, 6

We can create a list of random numbers between 1 and 6, inclusive.

1, 2, 3, 4, 5, 6

We can then use these numbers to select individuals from the population. For example, we could select the third number in the list, which would give us the number 3. This would then correspond to the third person in the population, which would be the person with the number 3.