Random Sampling: Overview, Questions, Preparation

Random sampling is a way of choosing samples of observations from the population to make assumptions about it. It is commonly known as probability sampling.

Various Types of Random Sampling 

In random sampling, every suitable individual has the probability of selecting the sample from the entire space, although it is an expensive and time-consuming method. There are four types of random sampling methods; they are as follows:

• Systematic sampling
• Simple random sampling
• Clustered sampling
• Stratified sampling

We will discuss each of them briefly.

Systematic Random Sampling

In this type of sampling, items are selected from the population by randomly choosing the selecting point. It’s equivalent to the ratio of the total population size and required population size.

Simple Random Sampling 

In this method, every item in the population has an equal probability of getting chosen in the sample. Because the selection of an item depends on the probability or possibility, this method is also known as chance selection. Generally, the sample size is quite large, and the items are randomly selected. Therefore, it is also called representative sampling.

Clustered Sampling

This one is quite similar to stratified sampling. Here, the population is divided into large subgroups. Then, some groups are chosen randomly, and simple random samples are gathered in the subgroups. The subgroups are also called clusters. This method is generally used to reduce the cost of data compilation.

Stratified Random Sampling

In this method, the population is divided into subgroups to get a simple random sample from every group and complete the process. The subgroups are also known as strata. It is created based on some features of the population. 

It is an essential topic in Probability that holds importance in higher education as well. The chapter holds a weightage of 10 marks in the exam.

The Formula for Random Sampling

Probability of getting a sample selected only one time is:

P = 1 – (N-1/N).(N-2/N-1)…..(N-n/N-(n-1))

Cancelling = 1-(N-n/n)

P = n/N

Probability of getting a sample selected more than once

P = 1-(1-(1/N))n

1.Every student of the college has an enrollment number. The admin has computer-generated 202020 Random numbers on those students that are to be asked to be a part of a survey. What type of sample is this?

Solution. It is stratified random sampling.

2.A hotel chain wants to survey the visitors that they randomly send a questionnaire on a day and survey the visitors on the venue. What type of sampling is this?

Solution.  It is a cluster sample.

3.If there are a thousand employees, and a hundred of them are selected for on-site work. The names will be put in a basket, and then a hundred names will be pulled out. What will be the probability of getting selected for each employee?

Solution.

Probability of each employee of getting selected once:

P = n/N = 100/1000 = 10%

Probability of each employee getting selected more than once:

P = 1-(1-(1/N))n

P = 1 – (999/1000)100

P = 0.952 or 9.5%

Q: What is the meaning of a random sample?

Q: How many types of random sampling are there?

Q: What is the formula for the probability of getting a sample selected only once?

Q: What is the formula for the probability of getting a sample selected more than once?

Q: What is systematic random sampling?