What is Statistics?

Here are some definitions

• a collection of procedures and principles for gaining information in order to make decisions when faced with uncertainty (J. Utts)

• a way of taming uncertainty, of turning raw data into arguments that can resolve profound questions (T. Amabile)

• the science of gaining information from numerical data (D.S. Moore)

• the explanation of variation in the context of what remains unexplained (D. Kaplan)

• the science of drawing conclusions from data with the aid of the mathematics of probability (S. Garfunkel)

• the mathematics of the collection, organization, and interpretation of numerical data, especially the analysis of a population's characteristics by inference from sampling (American Heritage Dictionary)

Some Similarities

1. Data -- the raw material

   Data are the raw material for doing statistics. We will learn more about different types of data, how to collect data, and how to summarize data as we go along.

2. Information -- the goal

   The goal is to gain information, to make decisions, to draw conclusions. "Raw" data conceals its message, we use statistics to reveal it.

3. Uncertainty -- the context

   Most often, we are concerned with gaining information about something other than what we have collected data about:

   • Baseball players with high batting averages or home run totals are paid well not because of the hits they have already had but because the owners hope this is indicative of future performance.

   • Public opion polling agencies don't particularly want to know the opinions of those they survey, they want an indication of the opinions of many unasked people.

   • Ford crash tests cars to insure safety, but we would rather buy a vehicle that was not part of the experiment than one that was. What does the crash test say about our cars?

   In such cases, there is a degree of uncertainty.

4. Probability -- the tool

   Statistics uses the mathematics of probability to measure and quantify the level of uncertainty, letting us know just what we can infer from the data -- and what we can't.

This page maintained by:
Randall Pruim
Department of Mathematics and Statistics
Calvin College
rpruim@calvin.edu