# What is a Sample in Statistics?

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Statistics is a mathematical concept that involves collecting, presenting, studying, and analyzing data collected for a specific purpose. Statistics is vital in the field of social studies, economics, business, and psychology. Statistics is applied to a sample set and not to a large group of data because of some obvious reasons:

• It is impractical and impossible to collect data corresponding to the large group of data required for a specific purpose.
• It requires a lot of extra time and effort.
• It would be a very costly task to collect data.

So, applying statistics to the sample set is always a better option to draw conclusions and interpretations. Statistical methods are of 2 types concerning the findings made from the data:

1. Descriptive Statistics: Statistics are used to conclude a sample set of data through mean, variance, and standard deviation.
2. Inferential Statistics: It is a statistical method where data collected is a subset of a larger population. The conclusions drawn from that sample data are used to conclude the more massive population data. For example, the average heights of 200 Army candidates are used to figure the average size of army candidates around India.

What is a Sample?

What are the benefits of using Sample?

What are the different types of Sampling used in Statistics?

What are the characteristics of reliable sample data?

How to choose the best Sample for the study?

What are the different types of Sampling errors, and how to avoid making these errors?

You will have some questions in your mind when we are talking about using sample data in statistics. All of these questions and other doubts you have related to statistics will get clarified as you read further. So, let’s first define the sample and the benefits of using sample data rather than the actual population data.

## What is a Sample? Why is it useful to use Sample data over the whole population data?

Sample refers to smaller parts of the population or a larger group of data. Sampling methods are used in humanities, medical, manufacturing, auditing, statistics, etc. It is a manageable part of a larger group or a whole population. Here, community means larger portions or groups of animals, products, humans, entries and data, while sample is a part or smaller fraction of the actual group. For example, a random sample of 100 items is tested out of the whole lot of 500 to check if it is in working condition and is of good quality. Sample data is used here to analyze the population data and would take a lot of effort and also a costlier task. So, it is advisable to use sample data over the actual group data to draw useful conclusions.

Benefits of using Sample:

• It makes the task less costly as in the example, testing 500 items would be more expensive, and using the sample data saved some money.
• Using sample data allows people or researchers to conduct their studies efficiently.
• It takes less time to study, analyze, and draw conclusions about the sample data.

## Different types of sampling methods used in Statistics

Sampling methods used in Statistics is of 2 types:

Simple random sampling: This sampling method is best suited when every item, person, or product is treated identically. Simple random sampling is an excellent technique if you do not care about the sample item type.  For example, if there are 2 items: A and B, simple random sampling is useful if you do not care that the sample data of 100 things is ultimately A or B or a mixture of A and B. The basic concept of simple random sampling is that every individual entity has the same probability of being selected for the sample data. It requires an unbiased selection of a sample that accurately represents the population.

• It is the simplest method of sampling, which does not need any advanced knowledge.
• Sample data selected must be unbiased, where each individual has the same probability of being selected.
• Such type of sampling has zero or negligible classification error.
• It is easier to analyze data collected using this method.

• Though the selection is unbiased, it may or may not correctly represent the whole population. For example, You are using this method to select a sample for CAT applicants, which has males to females ratio of 60:40. This method might select all males or a significantly less portion of females, which is not an accurate representation of the population.
• It is only reliable if not much information is available about the data or the cost of sampling is less. This method allows us to draw external conclusions about the data but is not useful in making effective, efficient, and essential data conclusions.

Stratified random sampling: In this type of sampling, the population data is divided into smaller groups or portions with individuals sharing similar or closer characteristics. Layer or strata is created for specific traits or factors, researchers want to study and a sample is randomly selected from the created strata. It reduces the chances of sampling errors. The conclusions drawn from stratified sampling are better in terms of effectiveness, efficiency, and variability from the actual population data. For example, there are 100 items of product A, 200 items of product B, 300 items of product C, and the sample size is 60 items. If you use simple random sampling to select 60 items, there are chances of poor selection where all selected items are majorly from product C. Still, if we use a stratified sampling method to select a sample, it will include 10 random sections from product A, 20 random selections from product B, and 30 random selections from product C. This way, there are lesser chances of sampling errors, and a balanced sample is created.

• It is the best sampling method if individuals in the population data have heterogeneous features.
• It creates a balanced sample where specific characteristics or features are also kept in mind to select strata or layers.
• There are lesser chances of sampling errors.
• Sample very closely represents the population.
• Grouping of items in strata makes it more manageable and even cheaper.

• If the data varies significantly, then forming a sample using proportionate strata or layer is not possible.
• It is a lengthier process of creating sample data, unlike the simple random sampling method.
• It is not useful when data is homogeneous.

## Criteria to select the sampling method:

While selecting the sampling method and creating a sample, the following criteria are taken into account:

• Cost or budget of forming a sample: Your sampling method depends upon the cost or budget allocated to create a model. It will help to get sample data from the population.
• Time and effort you want to put in for creating a sample.
• Size of the actual population data.
• Sampling error is allowed for analysis and concluding.
• It depends upon the nature of population data being used for research. It might be heterogeneous or homogeneous.

Sampling and Non-Sampling Errors:

We talked about sampling errors and making such errors while choosing a sample and the best sampling method, but we still do not know what sampling errors are.

So, sampling errors are the errors that exist when a researcher does not select the correct sample which represents the population and the conclusions drawn from the sample data do not match with the actual population data conclusions. There are two ways to reduce or minimize sampling errors:

• Increase the size of the sample of observations.
• We are selecting an unbiased random sample from the population data, which ultimately represents the population data.

Another kind of error might exist in sampling, which is known as non-sampling errors. These errors exist due to human mistakes like errors made while collecting data and forming a survey. It includes all errors other than sampling errors that might exist in creating a sample. Unlike sampling errors, it is challenging to reduce non-sampling errors as they are challenging to detect. There always exists a chance that a respondent may answer false or wrong information while filling the research survey.

Conclusion:

We are well aware of sample formation and different sampling methods used in statistics. We can now create sample data from population data keeping in mind the criteria of choosing the best sampling method and conditions of reliable sample data. Try eliminating or minimizing errors to acceptable limits to draw a useful and efficient conclusion from the data. Sometimes the data is too large, and you might need Data Tips and Tricks to analyze the information correctly and draw some important and useful conclusions from it. Cuemaths helps you learn some essential tips and tricks that allow you to analyze statistical data collected from sample data better and efficiently.