With probability, ORSAs learn how to develop models and make predictions of the relative likelihood of individual events happening within these models. Statistics, on the other hand, takes a given sample of data and tries to predict the model that produced the data to make inferences about general population the sample represents. Kalid Azad, the creator of the Better Explained blog, has a great article that provides an excellent analogy describing the relationship between probability and statistics. In short, probability is taking measurements of an animal, and deduce what kind of tracks they would leave. Conversely, a statistician will find a footprint and determine which type of animal produced it.
For ORSAs, statistics is our Swiss Army Knife. We will collect descriptive statistics of the data to find out parameters such as the mean, standard deviation, and other items to get a sense of the structure of the data and the types of data we can use for further analysis. From there we will explore the data visually and otherwise, and depending on the problem, conduct more prescriptive statistics to develop analytics. In other words, we look through data and glean out the most critical aspects of that data to give insights that were not obvious before the analysis. The tutorials and publications in this section will provide some examples of how we do that. In addition to the mathematics listed in the probability modeling section, you will also need to learn linear algebra.