What is a probability distribution?

A probability distribution is fundamentally a mathematical function that provides the probabilities of occurrence of different possible outcomes for a random variable. It encompasses all potential values that the random variable can take along with their associated probabilities. This means that option B accurately captures the essence of a probability distribution by stating that it represents all possible values of a random variable, showing how likely each of those values is to occur.

Understanding this concept is essential in statistics because it forms the basis for probability theory and informs various applications, such as risk modeling, decision-making under uncertainty, and predictive analysis. Probability distributions can take various forms, including discrete distributions (like the binomial or Poisson distributions) for specific outcomes and continuous distributions (like the normal or exponential distributions) for ranges of outcomes.

In contrast, the other options do not accurately describe what a probability distribution is. For instance, categorizing data or summarizing extremes does not reflect the probabilistic nature of potential outcomes associated with a random variable. Additionally, measures of central tendency, such as mean or median, represent specific characteristics of a data set but do not encompass the full probabilities associated with all potential outcomes of the variable. Hence, option B is the most precise definition of a probability distribution.