Difference Between Probability and Statistics

Probability vs Statistics

Probability is a measure of the likelihood of an event to occur. Since probability is a quantified measure, it has to be developed with the mathematical background. Specifically, this mathematical build of the probability is known as the probability theory. Statistics is the discipline of collection, organization, analysis, interpretation, and presentation of data. Most statistical models are based on experiments and hypotheses, and probability is integrated into the theory, to explain the scenarios better.

More about Probability

The simple heuristic application of the concept of probability is given a solid mathematical foundation by introducing axiomatic definitions. In this sense, probability is the study of the random phenomena, where it is centralized in the random variables, stochastic processes, and events.

In probability, a prediction is made based on a general model, which satisfies all aspects of the problem. This enables to quantify the uncertainty and the likelihood of occurrence of events in the scenario. Probability distribution functions are used to describe the probability of all possible events in the considered problem.

Another investigation in probability is the causality of events. Bayesian probability describes the likelihood of prior events based on the probability of the events caused by the events. This form is useful in artificial intelligence, especially in machine learning techniques.

More about Statistics

Statistics is considered as a branch of mathematics and a mathematical body with a scientific background. Because of the empirical nature of basics and its application oriented usage, it is not categorized as a pure mathematical subject.

Statistics supports theories for collection, analysis, and interpretation of data. The descriptive statistics and inferential statistics can be considered as a major division in statistics. Descriptive statistics is the branch of statistics which describe the main properties of a data set quantitatively. Inferential statistics is the branch of statistics, which derive conclusions about the concerned population from the data set obtained from a sample, subjected to random, observational, and sampling variations.

Descriptive statistics summarizes the data while inferential statistics is used to make forecasts and prediction, in general, about the population, from which the random sample was selected.

What is the difference between Probability and Statistics?

• Probability and statistics can be considered two opposite processes, or rather two inverse processes.

• Using probability theory, the randomness or uncertainty of a system is measured by means of its random variables. As a result of the comprehensive model developed, the behaviour of the individual elements can be predicted. But in statistics, a small number of observations is used to predict the behaviour of a larger set whereas, in probability, limited observations are selected at random from the population (the larger set).

• More clearly, it can be stated that using probability theory the general results can be used to interpret individual events, and the properties of the population are used to determine the properties of a smaller set. The probability model provides the data regarding the population.

• In statistics, the general model is based on specific events, and the sample properties are used to infer the characteristics of the population. Also, the statistical model is based on the observations/ data.

  • Grant Izmirlian

    Written by someone with a poor understanding of the most basic course on each subject.

  • Grant Izmirlian

    Statistics and probability theory are not “opposites”– rather statistics is one of the disciplines that formed the impetus for research of probabilists during the early 20th century, and probability theory — at least in the form of the theory of distributions and the basic limit laws (law of large numbers, and central limit theorem) form the backbone of statistics. A more practical question would be to ask what differences exist between the work of contemporary statisticians and contemporary probabilists. The answer to that is that yes, statisticians are concerned primarily with describing data. They use either parametric models based upon mathematical probability distiributions or non-parametric approaches based upon empirical distributions (harder). Their interests center on bias, precision and reproducibility. Modern probabilists have moved on from mathematical statistics. One active area is concerned primarily verifying probabilistic conjectures in physics. Most notably, probabilists are concerned with proving limit theorems, finding bounds in the limit for distributions arising in complex systems and the like.