[Maths Class Notes] on Random Sampling Pdf for Exam

It is impossible to study the whole population while performing a survey. Hence, the method of sampling allows researchers to gather information about a whole population based on the data collected from a subset. However, it is imperative to select an individual who will represent that demographic.

There are various sampling techniques available, which can be categorised into two groups, probability and non-probability sampling. The difference between these two depends on whether samples are randomly selected or not.

Probability sampling, which is also known as random sampling, begins with a complete set of eligible candidates, who have an equal chance to be a part of this survey. Moreover, this selection must be random, and they are no different than the individuals not sampled.

Types of Random Sampling

Random sampling is an essential process for any survey, as it contains essential data that help researchers to predict and decide the outcome of any forthcoming event. Here are some of the vital classifications of this process –

1. Simple Random Sampling

Simple random sampling meaning is the simplest way to get random samples. It involves selecting the desired sample size and also picking observations from people in a way that everyone has an identical chance of getting selected until the final sample size is finalised. For example, a random assortment of 20 students out of the total 50 of a single class provides a probability of being selected is 1/50.

2. Stratified Random Sampling

The focus of a random stratified sample is on dividing the whole database into important subgroups or strata. Moreover, the elements are arbitrarily selected from every stratum. For instance, one needs to achieve a sample size of 200, and have four groups to choose from, then selecting 50 samples from each group will suffice.

Now, the needed sample size will have a design that will match the population size or represent its sub-categories. The primary benefit of using this method over a simple random sampling method is that it offers a more focused approach towards selecting samples.

3. Cluster Sampling

The methods of random sampling offer a unique approach to this process. Here, samples are distributed among large sub-groups, and some of them get selected randomly. After that, researchers select samples randomly from these subgroups. These groups are known as clusters.

The primary reason for deciding on this method is to reduce data collection costs. Based on the ease of access, clusters get their definition. For instance, a borough can be a cluster in case of door-to-door sampling.

4. Multi-stage Sampling

This method of sample collection combines two or more types of sample design mentioned above. At first, the entire database is divided into different sub-groups, and then they are further classified into various subgroups, based on their similarities.

After that, one or more clusters receive a random selection depending on the stratum they belong to. Now, this process continues until this cluster cannot sustain any further division.

The Formula of Random Sampling

The formula of random sampling is, if that sample gets selected only once, P = 1 – (N-1/N)(N-2/N-1)…..(N-n/N-(n-1)).

Here P is a probability, n is the sample size, and N represents the population.

Now if one cancels 1-(N-n/n), it will provide P = n/N.

Moreover, the chance of a sample getting selected more than once is needed: P = 1-(1-(1/N)) n.

Example of Random Sampling

Assume a firm with 1000 employees, of the 100 are needed to complete an onsite work. Now all their names are in the basket and 100 will be picked from those. Now, in this instance, every employee has an equal chance of getting selected.

From this database, one can easily select the probability, once the sample size and population is available. Here is the calculation –

The chance of one-time selection is: P = n/N = 100/1000 = 10%

And, for more than once –

Random sampling is important to draw an unbiased conclusion from a large pool of data. It reduces the chances of any mistake and makes this process swift. This is one of the most important concepts of statistics that students need to comprehend to excel in their final exam.

Random sampling in statistics is available on the website of , one of India’s leading e-learning platforms. Students can download study materials with a lucid explanation of topics and detailed examples. Moreover, the live online classes and doubt clearing sessions further assist students in this regard.