A universe, in statistics, refers to a population comprising the units or informants of data, whether animate or inanimate, relating to a problem under study. In other words, it is the totality of the phenomenon studied or the set of objects of a statistical investigation.

Thus, when secondary data are not available for the problem being studied, the decision can be made to correct the primary data using any appropriate method. The required information can also be obtained using the following methods, namely the census method and the sample method.

For example, if we are going to study the average expenditure made by the students of a certain school that consists of 5,000 students, the universe, in this case, will be the "school" that consists of all the 5,000 students and the unit or the informant, in that case, will be each of these 5,000 students belonging to that school.

## Types of Universe

### Finite universe

The finite universe is one in which the number of units of information is defined and limited. For example, the "college" cited above is a finite universe, since in this case the number of units of information, i.e. students, is defined and limited, i.e. 5000.

### Infinite Universe

An infinite universe refers to a population in which the number of units that compose it cannot be definitively determined. For example, the population of stars in the sky, the population of temperatures at various points in the atmosphere, the population of heights, weights and ages of people in a country are examples of infinite universe. In addition, if a universe is very large, it is also considered an infinite universe, like the number of leaves of a tree.

### Existing universe

An existing universe is one that already exists with all its units in the form of concrete objects. The researcher has nothing to do for its creation except its discovery and location. For example, a college, a university, a library, a country and a state, with their concrete objects, such as students, books and individuals, respectively, are examples of an existing universe. Such a universe, too, can be under a finite universe or under an infinite universe.

### Experimental universe

An experimental universe is one that is constituted through the experiments carried out by a researcher and that is no longer in existence. For example, a record made of the number of faces and tails obtained by flipping a coin for a number of times, say 100, 200 or 500 times is a case of experimental universe.

Similarly, a record made of the number of times the number "5" is obtained by rolling a die for a certain number of times is an example of an experimental universe.

In this case, the universe no longer exists, but is created by the researcher himself through his experiments for a number of times. An experimental universe is generally infinite in character, as there is no limit to the number of times experiments can be conducted to record the events of a particular event.

## Elementary Units

The attributes that are the object of study are called characteristics and the units that possess them are called elementary units. The set of such units is generally described as population. Thus, all units of any field of research constitute the universe and all elementary units (on the basis of one characteristic or more) constitute the population. Often, we do not find any difference between population and universe, so both terms are considered interchangeable. However, the researcher must necessarily define these terms precisely.

## Universe, Population and Sample

Universe, population and sample must be understood together. The Universe and the population can refer to the same thing and can be considered synonymous if the population that is used when choosing the samples includes all members of the universe. If you have data from all the members of the universe, then your population is the universe and you are actually taking samples from the universe.

However, if you only have data from some members of the universe, your population is just those members of the universe and you are sampling those members of the universe whose data you have access to. For example, let's say you're conducting research on 10 million workers in Country X. His universe is all workers. If you have access to the social security number of all the workers from whom you can draw your sample of 10,000 workers, then your universe and your population are the same. If it only has access to the social security numbers of 1 million workers, its universe is 10 million workers, its population is 1 million workers and its sample is 10,000 workers.

### Population

A population is a distinct group of individuals, either a nation or a group of people with a common characteristic. In statistics, a population is the set of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common characteristic can be said to be a population.

In most usages, the word population implies a group of people or, at least, a group of living things. However, statisticians refer to any group they are studying as a population. The population of a study may be babies born in North America in 2021, the total number of tech companies in Asia since 2000, the average height of all accounting test candidates, or the median weight of U.S. taxpayers.

#### Finite and Infinite Population

The population or the universe can be finite or infinite. The population is said to be finite if it is made up of a fixed number of elements, so it is possible to list it in its entirety. For example, the population of a city or the number of workers in a factory are examples of finite populations. The symbol "N" is generally used to indicate how many elements (or items) there are in the case of a finite population.

An infinite population is one in which it is theoretically impossible to observe all the elements. Therefore, in an infinite population the number of elements is infinite, that is, we cannot have any idea about the total number of elements. The number of stars in a sky, the possible rolls of a pair of dice are examples of infinite population. It must be remembered that there is no truly infinite population of physical objects, even though many of those populations appear to be very large. From a practical point of view, we use the term infinite population for a population that cannot be enumerated in a reasonable period of time. In this way, we use the theoretical concept of infinite population as an approximation to a very large finite population.

Statisticians and researchers prefer to know the characteristics of each entity in a population in order to draw the most precise conclusions possible. However, this is impossible or impractical most of the time, as population sets are usually quite large.

### Sample

Sampling, in statistics, process or method to extract a representative group of individuals or cases from a given population. Sampling and statistical inference are used in circumstances where it is not practical to obtain information from each member of the population, such as in biological or chemical analysis, industrial quality control or social surveys.

### Simple Random Sampling

The basic design of sampling is simple random sampling, based on probability theory. In this form of random sampling, each element of the sampled population has the same probability of being selected. In a random sample of a class of 50 students, for example, each student has the same probability, 1/50, of being selected. Each combination of elements extracted from the population also has the same probability of being selected.

### Probabilistic Sampling

Sampling based on probability theory allows the researcher to determine the probability that the statistical results are the result of chance. The most commonly used methods, which perfect this basic idea, are stratified sampling (in which the population is divided into classes and simple random samples are drawn from each class), cluster sampling (in which the unit of the sample is a group, such as a household) and systematic sampling (samples taken by any system other than random choice, as one in ten names on a list).

### Trial Sampling

An alternative to probabilistic sampling is trial sampling, in which selection is based on the judgment of the investigator and there is an unknown probability of inclusion in the sample for any case. Probabilistic methods are usually preferred because they avoid selection bias and allow sampling error to be estimated (the difference between the measurement obtained from the sample and that of the entire population from which the sample was extracted).

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