Statistics and Data

There is a general confusion about the meaning of “statistics.” If we look at the American Heritage Dictionary of the English Language, we find two very different definitions of statistics.

Statistics is a collection of numerical data.
Statistics is the mathematics of the collection, organization, and interpretation of numerical data.

Let's focus first on the first definition. To many people, statistics are simply numbers like

61, 73, .406

But these are not statistics, they are simply numbers. Statistics are numbers with a context or underlying meaning. The author is a baseball fan and the above three numbers have interesting contexts:

61 is the number of home runs hit by Roger Maris in 1961
73 is the number of home runs hit by Barry Bonds in 2001
.406 is the batting of Ted Williams in 1941 (the last player to have a batting average of over .400 for a single season)

A baseball fan cares about these statistics since they make him or her think about outstanding baseball players and their accomplishments.

We will refer to information collected from people or objects as data. Actually, data is the plural form and a single piece of information is called datum, although data is now commonly used to represent one or more pieces of information.

Why Do We Collect Data?

Why do we care about data? We collect data to help us learn about our world. We start off with some questions about something we wish to learn about, and we find appropriate data to help us answer these questions.

The Second Definition of Statistics

We've seen that statistics are numerical data that we work with. But statistics has a second deeper meaning -- it's the science of using these data to learn about our world and make conclusions.

The science of statistics has four basic components:

FORMULATING QUESTIONS: First, state some questions or problems that we would like to address by collecting relevant data.
COLLECTING DATA: Second, specify effective ways of collecting data that are useful in answering the questions of interest.
ORGANIZING & SUMMARIZING: Next, organize and summarize the collected data to learn about its general features.
MAKING CONCLUSIONS: Last, use the data to make conclusions. (It turns out that probability or chance plays an important role in decision-making.)

Any statistical study reported in the media will have these four components. At the beginning, there will be some questions that motivated the researcher to study a problem. If there were no questions, then there would be no reason to proceed further into a statistical study. Second, the researcher will collect data that he or she believes will be useful in answering the question. We will see that data can be collected or found from many sources. Next the researcher organizes the data in some useful way and make graphs and or calculations that are helpful in answering the main questions. Finally, the researcher has to use the graphs and calculations to address the questions of interest. It is possible that the data are insufficient or inconclusive on answering the questions and perhaps a new statistical study will be undertaken.

In this topic, we illustrate the four components of a statistical study for several examples. We begin with a description of our own study on learning about the educational achievement of Americans and then we look at statistical studies reported in the media.