# CHAPTER 24

# Data Analysis.Probability Theory

We first show how to handle data numerically or in terms of graphs, and how to extract information (average size, spread of data, etc.) from them. If these data are influenced by “chance,” by factors whose effect we cannot predict exactly (e.g., weather data, stock prices, life spans of tires, etc.), we have to rely on **probability theory**. This theory originated in games of chance, such as flipping coins, rolling dice, or playing cards. Nowadays it gives mathematical models of chance processes called *random experiments* or, briefly, **experiments**. In such an experiment we observe a **random variable** *X*, that is, a function whose values in a **trial** (a performance of an experiment) occur “by chance” (Sec. 24.3) according to a **probability distribution** that gives the individual probabilities with which possible values of *X* may occur in the long run. (Example: Each of the six faces of a die should occur with the same probability, 1/6.) Or we may simultaneously observe more than one random variable, for instance, height *and* weight of persons or hardness *and* tensile strength of steel. This is discussed in Sec. 24.9, which will also give the basis for the mathematical justification of the statistical methods in Chapter 25.

*Prerequisite:* Calculus.

*References and Answers to Problems:* App. 1 Part G, App. 2.

## 24.1 Data Representation. Average. Spread

Data ...