What Is a Population in Statistics?

Introduction 

Once a renowned statistician said that facts are stubborn and statistics are limber. The aegis of statistics is deep and full of discoveries. With the help of statistical knowledge, you can collect data, employ analysis, make discoveries, derive conclusions, and make predictions about the future. It is the grammar of science.

Statistics assist you in better cognizance of the subject matter. Today statistics hold immense value in the study of various other subjects like mathematics, biology, etc. Statistics not only deal with numbers and facts but also allow you to gauge the claim based on quantitative evidence. Have you ever thought that the world gets mitts on more data and information to influence you than never before?

One of the cardinal aspects of statistics is population. In statistics, data get composed, collected, and selected for statistical study with the help of guidelines and procedures. There are two types of data sets – Population and Sample. Both are helpful in the calculation of mean deviation, variance, and standard deviation. For Example – If a population can get expressed by N then, the sample size of that population will be n- 1. While studying the concepts, we usually face the following questions –

What is Statistics? 

What is a population in statistics? 

What is the importance of the population? 

How many types of the population are there? 

If you are also combating these questions, at that point, you are not alone. No compelling reason to get fearful and let us endeavor to grasp the topic in detail.

Meaning of Population 

When we talk about the population, we refer to the total number of people living in a city, town, or country. But in statistics, it has a different and unique meaning. The population refers to the sets of observations that can be curated. It means the entire horde of people, groups, objects, items, and events from which a statistical sample gets procured. It means all statistics entities from which statistical inferences are obtained. A sample is the data accumulated from the population-based on rules and codes of procedure. There are two concepts used in population calculation in statistics. They are:

 

  • Population Samples 

 

A sample is a small group drawn out from the population having the features of the entire population. It helps to avoid the study of large populations and save efforts and time of statisticians. The hypothesis can get procured on population samples that resonated with the whole population. In statistical language, a sample is denoted by n.

 

  • Population Parameters

 

Population parameters mean when the data become dependent on the entire population. When the population can use it to find out the averages and deviations, it gets referred to as parameters. The population mean and the standard deviation is usually denoted;

Population deviation – µ

Population Mean- σ

The deviation in the variation in the population can usually be termed as population standard deviation. Whenever you have to divide the standard deviation by the square root of the number of perceptions in a sample, the outcome gets termed as the standard error of the mean.

With the help of the statistical population, the statistician can study behavior, drifts, and make observations. It even helps to derive the required conclusions about the individuals, plants, even celestial bodies like planets and stars.

Sub-population 

A subset of a populace is known as a sub-population. The population gets termed as heterogeneous when the properties of the population are different. In such a case, the entire population can often be studied and analyzed. Like, a medicine may have distinct effects on individuals, these effects can get excluded from the entire population or studied in isolation.

One can easily study parameters if the population is divided into various subsets. If the height of the population needs to be calculated, it would be convenient to study the population divided into males and females.

Constituents of the Population 

Everything without exception can be a piece of the populace until each comprises a typical element that may get gathered to lead a study. For example, in an examination that targets to study the mean height of each individual of 40 years of age males in Australia, the populace is obscure and explicit that relies upon the topic and a definitive objective of the investigation.

A Real-World Example of a Population 

Let us try to understand the population with the help of an example. Suppose you are the owner of a shirt apparel shop. You have produced a total of 5000 shirts for exporting to England. But before shipping them, you want to have a quality check to ensure that everything is fine and up-to-date. It will not be cost-effective and excessive time consuming to check each shirt. Instead, you can check and analyze the 100 samples of shirts as a cumulative representation of the population. Therefore, you can ensure and conclude the quality of all shirts. Here, what did you observe? A population can get resonated with the samples.

5000 shirts – Population

100 shirts– Sample

Types of population 

There are four types of population. They are as follows:

  • Finite Population– As the name suggests, when the population can easily be counted and analyzed, it is called a finite population or countable population. In a nutshell, it means that objects, data, or individuals are enumerable in the population. For example, the number of births and deaths per year or the number of words in an article.
  • Infinite Population- It is the reverse of a finite population. When we can’t measure the objects, data, or individuals, it is called an infinite population. Here, the population size is relatively enormous to count or measure. It demands lots of time and effort on the part of researchers to study and analyze each population. For instance, the total number of fishes in the world.
  • Existent Population- When the individual or units are present in concrete form, it is termed as an existent population. It means that data is available in solid shape for study and analysis. Books and students are classic examples.

 Hypothetical Population- When units lack solid form and cannot get counted, it will be a hypothetical population. This type of population is based on observation, prediction, or associated with homogeneity factors. For example, results from tossing a coin.

Population Mean 

The population mean is often defined as the average of group characteristics. The group refers to any individual, object, item, or person. There should be at least one interest or attribute in common to calculate the population means. In statistics, the population mean is a rare phenomenon because it is time-consuming and expensive in nature. It can only be utilized in extensive statistics studies.

The statistics depend on utilizing information from an irregular sample that is illustrative of the populace on the loose. From that sample mean, we can deduce things about the greater population mean.

For example –

  • In a University of 5000 students, the average CGPA is 4.5

The formula to identify the population mean is:

μ = (Σ * X)/ N

Where:

Σ = the sum of

X = all the individual items.

N = number of items.

Types of Sampling 

In order to study a population subset thoroughly, it is mandatory to learn the meaning and types of sampling methods used in the population. We have already discussed the sample above. There are three types of sampling, namely:

  • Simple Random Sampling- One of the most widely recognized sampling strategies is a basic irregular example, otherwise called a simple random sample. The sample size and people get picked arbitrarily so that each sample gathers a fair opportunity to get chosen for the examination/study.
  • Simple Stratified Sampling- When a population is large and has distinct features, they get classified into strata. Each stratum is beneficial for the researcher to conduct further study.
  • Cluster Sampling- When the population is segregated into groups. They are randomly selected which makes it useful and less time-consuming.

Conclusion  

As we can conclude that the population has a paramount role to play in statistics, and for better apprehension, one must get deeper insights about the subject matter. Do you know that in the USA, July 11th is celebrated as World Population Day? In statistics, the population is the only way through which the sample can be derived and studied. Data gleaned should be credible and authentic to get bonafide results. It is all about data. It is outrightly data based. To know more about data, do visit Types of Data with Examples in Cuemath style.

Indeed, Cuemath offers customized learning material for each understudy and puts efforts and dedication into creating an ardent learning establishment where students are math-cherishing instead of math dreading. Their only mission is to lead the path in constructing mathematical thinking in kids to empower them to transform into the obstacle solvers and creative masterminds of the future. Happy Learning!!

In the event that you have doubts or have any inquiries regarding the population in statistics, kindly comment beneath and let us answer it!

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