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 whole, instead of the whole, 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. Approaching 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 its study are extended to the population, without significant loss of information..
| Population | Show | |
| Definition | The set of all the elements considered for a study. | It is a part of the population, selected to be representative and thus facilitate its analysis. |
| Symbol | Population size: N | Sample size: n |
| Analysis | Has parameters, such as descriptive values. | It is analyzed using statistics. |
| Examples | Total number of birds that inhabit a forest. | For an investigation 1000 birds are taken from a forest. |
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, events and ideas..
Examples of populations of diverse nature are:
-Air molecules inside a sealed container.
-All the stars in the Milky Way.
-The birds that populate a forest.
-The total number of trees in that same or another forest.
-The set of subscribers of a telephone company that has branches in America and Europe.
-The tosses that we make of a coin.
-The number of bacteria in a culture.
-The monthly production of screws in a factory.
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. Instead, 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.
Suppose you have 20 marbles in a box and sample 2 marbles without replacement. Eventually the marbles in the box will run out, therefore 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..
What happens if every time we extract a sample of marbles we return them to the box after observing them? In that case we can take an infinite number of samples, and in this way consider that the population of marbles is infinite.
Another example of an infinite population we have in the toss of coins or dice, since in theory, you can take all the samples you want, without any limit.
Even a finite population known to contain a large number of elements can be considered infinite in practice, 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..
It is also important to know the chronological location of the population. It is not the same to study records of the inhabitants of a large city at the beginning of the 20th century than to do 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 ascertaining its homogeneity -or lack of it.-.
The sample is the set of elements selected from the population to represent it. The point of doing this, as we said, is to make the job easier. By handling less amount of data, less amount of resources are invested and faster results are obtained.
However, in order for it to function properly, the sample must be adequate. The selection process is carried out using sampling techniques that use mathematical criteria..
The sample drawn does not have to be unique. In fact, a population can give rise to several samples.
For example, suppose that the population is the set of students in a secondary school that has several sections for each grade. A representative sample should contain some 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 look at some more examples:
Department store owners want to estimate the average amount of money customers spend shopping. To do this, they collect all the invoices for a certain period, let's say a year.
The number of invoices for the last year is the population to be analyzed.
Now, if a completely random sample of 150 invoices is drawn from this group, it would already be the sample.
When elections approach, be it 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 registered voters in the corresponding electoral system..
Since it would take a lot of time and effort to locate and question each voter, the pollsters choose a sample of voters to survey and from there extract the percentages and determine the trends..
Selecting the appropriate sample is just the beginning, but it is a critical step in ensuring the success of the study..
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