Probability and Statistics – Concept, differences and characteristics

We explain what probability and statistics are, their fields of study and characteristics. Also, the types of statistics.

probability and statistics
Probability and statistics are tools to deal with random phenomena.

What are probability and statistics?

When we talk about probability and statistics, we commonly refer to study of chance from a mathematical point of view. That is, to the study of the formal laws that govern it, from two clearly differentiated points of view:

  • Probability It is understood as the degree of certainty that one has regarding whether an event occurs or not, and it is also a discipline in charge of making predictive models for random phenomena, in order to anticipate them and study their logical consequences.
  • StatisticsInstead, it offers its own methods and techniques to understand what these models mean, since it is an independent discipline, a branch of mathematics, focused on the study of variability.

Probability and statistics are closely linked, since they are the two great tools that humanity has to deal with random phenomena.

That is, they study those whose patterns of occurrence are beyond our perspectives or involve calculations that are too large and with too much margin of error to attempt to address them in a concrete way. Thus, the need to make models and approximations is imposed, and to work in terms of percentages of occurrence.


Probability is a field of study, to which the Theory of Probability is dedicated, a branch of mathematics that is widely used in disciplines such as mathematics, social sciences, finance, economics and, of course, statistics, to draw conclusions as to how likely an event is to occur, or not to occur.

The need for this type of study arose thanks to the desire of the human being to being able to predict the future with a certain margin of certainty, something that translates into the possibility of anticipating and avoiding catastrophes, for example. To do this, it proposes various laws and approximations that often allow the scientific calculation of what is considered probable, and that is often contrary to what our intuition tells us.


Statistics arose out of the need for the modern state to think and control its growing populations. That is the reason for its name, coming from Italian statista (“Statesman”) and by direct translation from German Statistik. At present, this discipline is useful for a myriad of sciences and applications, organized into two large areas of study:

  • Descriptive statistics, dedicated to visualizing, describing and summarizing numerically or graphically the information obtained from a set of statistical data.
  • Inferential statistics, dedicated to proposing models, predictions and inferences from the observations made around the randomness of a phenomenon.

Both branches are part of applied statistics, which aspires to solve problems about the probability of certain real matters. Something vital for decision making and future planning.