Statistics is about inferring probabilities from data such that we can make predictions (where data are discernible differences of some quantities). Inference m

Statistics is about inferring probabilities from data such that we can make predictions (where data are discernible differences of some quantities). Inference means finding out what the world is about using some sort of representation (a model). The entire project is basically concerned with (mostly lossy) compression: How to represent the complexity of the world such that we can reason about it with limited resources, i.e. estimate things we can't compute using things we can compute. If our statistic summarizes enough to allow us to make useful predictions, it is called a sufficient statistic. Probability is at the heart of the project: frequencies that summarize reoccurring data. Instead of storing a reoccurring pattern multiple times, we just store it once and record how often it has occurred.