Examining Distributions

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CHAPTER OUTLINE

  • 1.1 Data
  • 1.2 Displaying Distributions with Graphs
  • 1.3 Describing Distributions with Numbers
  • 1.4 Density Curves and the Normal Distributions

Introduction

Statistics is the science of learning from data. Data are numerical or qualitative descriptions of the objects that we want to study. In this chapter, we will master the art of examining data.

Data are used to inform decisions in business and economics in many different settings.

  • Why has the AC Nielsen company been studying the habits of customers since it was founded in 1923?
  • Who uses the databases of information maintained by the Better Business Bureau to make business decisions?
  • How can data collected by the U.S. Chamber of Commerce be analyzed to provide summaries used to evaluate business opportunities?

We begin in Section 1.1 with some basic ideas about data. We learn about the different types of data that are collected and how data sets are organized.

Section 1.2 starts our process of learning from data by looking at graphs. These visual displays give us a picture of the overall patterns in a set of data. We have excellent software tools that help us make these graphs. However, it takes a little experience and a lot of judgment to study the graphs carefully and to explain what they tell us about our data.

Section 1.3 continues our process of learning from data by computing numerical summaries. These sets of numbers describe key characteristics of the patterns that we saw in our graphical summaries.

A statistical model is an idealized framework that helps us to understand variables and relationships between variables. In the first three sections, we focus on numerical and graphical ways to describe data. In Section 1.4, the final section of this chapter, we introduce the idea of a density curve as a way to describe the distribution of a variable. The most important statistical model is the Normal distribution, which is introduced here. Normal distributions are used to describe many sets of data. They also play a fundamental role in the methods that we use to draw conclusions from many sets of data.