What is Statistics

Course Documentation

CJ Alverson

What is Statistics ? Stated informally,

Statistics is the process of describing characteristics of a sample of objects of interest. Statistics has two basic levels of activity - descriptive and inferential. Descriptive statistics is concerned with describing the sample. Inferential statistics is concerned with checking the plausibility of specific hypotheses against a sample.

Typically, applications of modern statistics involve both descriptive and inferential statistical methods.

The formal tools used in both types of Statistics come from Probability.

What is Probability ? Stated informally,

Probability is the branch of Mathematics concerned with modeling the likelihood of the occurrence of events. Probability models describe the likelihood 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.