STATISTICAL VARIABLES: TYPES AND EXAMPLES - DUDAS - 2025

The statistical variables are characteristics possessed people, things or places that can be measured. Examples of frequently used variables are age, weight, height, gender, marital status, academic level, temperature, the number of hours an incandescent bulb lasts, and many others.

One of the objectives of science is to know how the variables of a system behave in order to make predictions about its future behavior. According to its nature, each variable requires a specific treatment to obtain the maximum information from it.

The number of variables to study is enormous, but examining the aforementioned group carefully, we immediately notice that some can be expressed numerically, while others cannot.

This gives us grounds for an initial classification of statistical variables into two fundamental types: qualitative and numerical.

Types of statistical variables

- Qualitative variables

As the name implies, qualitative variables are used to designate categories or qualities.

A well-known example of this type of variable is marital status: single, married, divorced or widowed. Neither of these categories is greater than the other, it only designates a different situation.

More variables of this type are:

-Academic level

-Month of year

-Brand of car that is driven

-Profession

-Nationality

-Countries, cities, districts, counties and other territorial divisions.

A category can also be designated by a number, for example the telephone number, the house number, the street or the postal code, without this representing a numerical rating, but rather a label.

The street number is a qualitative variable, it is not a quantitative variable. Source: Pixabay.

Nominal, ordinal, and binary variables

The qualitative variables can be in turn:

- Nominals, which assign a name to the quality, such as the color for example.

- Ordinals, which represent order, as in the case of a scale of socioeconomic strata (high, medium, low) or opinions about some kind of proposal (in favor, indifferent, against). *

- Binary, also called dichotomous, there are only two possible values, such as sex. This variable can be assigned a numeric label, such as 1 and 2, without representing numerical evaluation or any kind of order.

* Some authors include ordinal variables in the group of quantitative variables, which are described below. It is because they express order or hierarchy.

- Numerical or quantitative variables

These variables are assigned a number, since they represent quantities, such as salary, age, distances, and test grades.

They are widely used to contrast preferences and estimate trends. They can be associated with qualitative variables and build bar graphs and histograms that facilitate visual analysis.

Some numerical variables can be transformed into qualitative variables, but the opposite is not possible. For example, the numerical variable “age” can be divided into intervals with assigned labels, such as infants, children, adolescents, adults and the elderly.

However, it should be noted that there are operations that can be done with numerical variables, which obviously cannot be carried out with qualitative ones, for example calculating averages and other statistical estimators.

If you want to do calculations, you have to keep the variable "age" as a numeric variable. But other applications may not require numerical detail, for these it would be enough to leave the labels named.

The numerical variables are divided into two large categories: discrete variables and continuous variables.

Discrete variables

Discrete variables only take certain values ​​and are characterized by being countable, for example the number of children in a family, the number of pets, the number of customers who visit a store every day, and subscribers to a cable company, to mention Some examples.

Defining for example the variable "number of pets", it takes its values ​​from the set of natural numbers. A person can have 0, 1, 2, 3 or more pets, but never 2.5 pets, for example.

However, a discrete variable necessarily has natural or integer values. Decimal numbers are also useful, since the criterion for determining whether a variable is discrete is whether it is countable or countable.

For example, suppose that the fraction of defective light bulbs in a factory, taken from a sample of 50, 100 or N light bulbs at random, is defined as a variable.

If no light bulbs are defective, the variable takes the value 0. But if 1 of N light bulbs is defective, the variable is 1 / N, if there are two defective it is 2 / N and so on until the event that the N light bulbs were defective and in that case the fraction would be 1.

Continuous variables

Unlike discrete variables, continuous variables can take any value. For example, the weight of students taking a certain subject, height, temperature, time, length and many more.

Pareto chart comparing defect frequency (quantitative variable on the vertical axis) and the cumulative percentage versus each defect on the horizontal axis (qualitative variable. Source: Wikimedia Commons.

As the continuous variable takes infinite values, all kinds of calculations can be made with it with the desired precision, just by adjusting the number of decimal places.

In practice there are continuous variables that can be expressed as discrete variables, for example the age of a person.

The exact age of a person can be counted in years, months, weeks, days and more, depending on the precision that is desired, but it is usually rounded in years and thus becomes discreet.

The income of a person is also a continuous variable, but it is usually better worked if intervals are established.

- Dependent and independent variables

The dependent variables are those that are measured during an experiment, to study the relationship they have with others, which would be considered the independent variables.

Example 1

In this example we are going to see the evolution of prices suffered by the pizzas of a food establishment depending on their size.

The dependent variable (y) would be the price, while the independent variable (x) would be the size. In this case, the small pizza costs € 9, the medium one € 12 and the family one € 15.

That is, as the size of the pizza increases, it costs more. Therefore, the price would be dependent on the size.

This function would be y = f (x)

Example 2

A simple example: we want to examine the effect produced by changes in the current I through a metal wire, for which the voltage V between the ends of this is measured.

The independent variable (the cause) is the current, while the dependent variable (the effect) is the voltage, whose value depends on the current that passes through the wire.

In the experiment, what is sought is to know what the law is like for V when I is varied. If the dependence of the voltage with the current turns out to be linear, that is: V ∝ I, the conductor is ohmic and the constant of proportionality is the resistance of the wire.

But the fact that a variable is independent in one experiment does not mean that it is so in another. This will depend on the phenomenon under study and the type of research to be carried out.

For example, the current I that passes through a closed conductor rotating in a constant magnetic field becomes the dependent variable with respect to time t, which would become the independent variable.

References

1. Berenson, M. 1985. Statistics for management and economics. Interamericana SA
2. Canavos, G. 1988. Probability and Statistics: Applications and methods. McGraw Hill.
3. Devore, J. 2012. Probability and Statistics for Engineering and Science. 8th. Edition. Cengage.
4. Economic Encyclopedia. Continuous variables. Recovered from: encyclopediaeconomica.com.
5. Levin, R. 1988. Statistics for Administrators. 2nd. Edition. Prentice Hall.
6. Walpole, R. 2007. Probability and Statistics for Engineering and Sciences. Pearson.