Statistics has two basic levels of activity - descriptive and inferential . Descriptive statisitics is concerned with describing the sample . Inferential statistics is concerned with checking the plausibility of specific hypotheses against a sample. The formal tools used in both types of Statistics come from Probability . Stated informally, Probability is the branch of Mathematics concerned with modeling the likelihood of the occurrence of events .
Probability models describe the likelihoods of specific events associated with specific processes.
For example, a simple probability model applies to the tosses of a coin. The starting point of this probability model is given by the likelihood that a particular face of the coin will show on a single toss. Descriptive statistics typically involves the estimation of probability models from samples. Inferential statistics typically involves checking a sample against a specific probability model . First we will learn something about Probability, and then we will learn something about Statistics.