The **differences between population and sample** In Statistics, they derive from the fact that the population is the universe of elements to be studied, while the sample is a representative part of the population.

Analyzing a sample taken from the set, instead of the entire set, represents a clear advantage in terms of information management. Let’s see in more detail the main differences between the two concepts below.

It is now clear that a population can consist of a very large set of elements: people, animals, microorganisms, or particles. Addressing the study of each of these elements separately consumes a large amount of resources, time and effort.

But by choosing a carefully selected sample, the results derived from your study are extended to the population, without significant loss of information.

The set of all elements considered for a study.

It is a part of the population, selected to be representative and thus facilitate its analysis.

Population size: N

It has parameters, such as descriptive values.

It is analyzed by statistics.

Total number of birds that inhabit a forest.

For an investigation, 1000 birds are taken from a forest.

**What is a population?**

In Statistics, the concept of population has a broader meaning than the everyday one. A population is associated with the number of inhabitants of a country or a city, however a statistical population can consist of people and living beings, but also large and small objects, particles, events, occurrences and ideas.

Examples of populations of diverse nature are:

-Air molecules inside a sealed container.

-The totality of the stars in the Milky Way.

-The birds that populate a forest.

-The total number of trees in the same or another forest.

-The set of subscribers of a telephone company that has branches in America and Europe.

-The throws that we make of a coin.

-The number of bacteria in a culture.

-The monthly production of screws in a factory.

**population characteristics**

We already know how diverse populations can be. Now let’s see how they can be classified according to their extension.

A finite quantity is one that can be expressed by a number, such as the number of marbles in a box. On the other hand, of an infinite quantity we cannot give a precise value.

This difference will allow us to define two types of populations according to their extension.

**finite populations**

Suppose you have 20 marbles in a box and you draw samples of 2 marbles without replacement. Eventually the marbles in the box will run out, so the population is finite.

A number can be finite even if it is very large. A culture of bacteria consists of a large number, but it is finite, like the number of stars in the galaxy or the molecules of a portion of gas enclosed in a container.

**infinite populations**

What if every time we draw a sample of marbles we put them back in the box after looking at them? In that case we can take an infinite number of samples, and thus consider that the population of marbles is infinite.

Another example of an infinite population is found in the toss of coins or dice, since in theory, all the samples you want can be taken, without any limit.

Even a finite population known to contain a large number of elements can be considered practically infinite, if necessary.

That is why it is very important to define the population carefully before undertaking the study, which means setting its limits, since its size will determine the shape and size of the samples that are drawn from it later.

**Other important features**

It is also important to know the chronological location of the population. Studying records of the inhabitants of a large city at the beginning of the 20th century is not the same as doing the same with the inhabitants of the same city at the beginning of the 21st century.

Likewise, the analyst must take care of taking into account the location of the population, as well as finding out its homogeneity –or lack of it-.

**What is a sample?**

The sample is the set of elements selected from among the population to represent it. The objective of doing this, as we said, is to facilitate the work. By handling less amount of data, fewer resources are invested and faster results are obtained.

However, for it to fulfill its function properly, the sample must be adequate. The selection process is carried out through sampling techniques that use mathematical criteria.

The extracted sample does not have to be unique. In fact, a population can give rise to different samples.

For example, suppose that the population is the set of students of a middle school that has several sections for each grade. A representative sample should contain a few students from each of the sections of each grade, for example those whose name begins with the letter A.

On the other hand, a not so representative sample could be if all the students of the same grade were chosen. Let’s see some more examples:

**Example 1**

The owners of a department store want to estimate the average amount of money that customers spend shopping. To do this, they collect all the invoices for a certain period, let’s say a year.

The number of invoices from the last year is the population to analyze.

Now, if a completely random sample of 150 invoices is drawn from this group, it would already be the sample.

**Example 2**

When elections approach, whether at the national or local level, political parties often hire specialized companies for data analysis. In this way they know the intention of the vote of the inhabitants and plan appropriate campaign strategies.

In this case, the population consists of the entire universe of voters registered in the corresponding electoral system.

Since it would take a lot of time and effort to locate and question each voter, pollsters choose a sample of voters to survey and from there they extract percentages and determine trends.

The selection of the appropriate sample is just the beginning, but it is a determining step to ensure the success of the study.

**References**

Berenson, M. 1985. Statistics for Administration and Economics, Concepts and Applications. Interamerican Editorial.

Brase/Brase. 2009. Understandable Statistics. 9th. Edition. Houghton Mifflin.

Devore, J. 2012. Probability and Statistics for Engineering and Science. 8th. Edition. Cengage Learning.

Galindo, E. 2011. Statistics, methods and applications. Prociencia Editors.

Levin, R. 1981. Statistics for Managers. Prentice Hall.

matmobile. Population and sample, examples and exercises. Recovered from: matemovil.com.