## Learning Math: Data Analysis, Statistics, and Probability

# Statistics As Problem Solving Part A: A Problem-Solving Process (15 minutes)

The word statistics may bring to mind polls and surveys, or facts and figures in a newspaper article. But statistics is more than just a bunch of numbers: Statistics is a problem-solving process that seeks answers to questions through data.

By asking and answering statistical questions, we can learn more about the world around us. Statistics is used every day to help us gain insight into questions that affect our lives: Is our population growing or shrinking? What is the safest way to invest money? Will eating more fruits and vegetables really make us live longer?

**Problem A1**

What do you think of when you hear the word *statistics?*

Four things make a problem statistical: the way in which you ask the question, the role and nature of the data, the particular ways in which you examine the data, and the types of interpretations you make from the investigation. A statistics problem typically contains four components:

**1. Ask a Question**

Asking a question gets the process started. It’s important to ask a question carefully, with an understanding of the data you will use to find your answer.

**2, Collect Data**

Collecting data to help answer the question is an important step in the process. You obtain data by measuring something, so your measurement methods must be chosen with care. Sampling is one way to collect data; experimentation is another.

**3. Analyze Data**

Data must be organized, summarized, and represented properly in order to provide good answers to statistical questions. Also, the data you collect usually vary (i.e., they are not all the same), and you will need to account for the sources of this variation.

**4. Interpret Results**

After you analyze your data, you must interpret it in order to provide an answer — or answers — to the original question.

This four-step process for solving statistical problems is the foundation of all the activities in this course. You will become increasingly familiar with this process as you investigate different statistical problems.

**Problem A2**

Here are two such general questions: “Are girls smarter than boys?” and “Which airline has the best on-time departure performance?”

Think of a general question that could be answered with statistics. Now think carefully about the four steps listed above. How would you carry out each step in order to answer your question? Be as specific as possible.

**Video Segment**

In this video segment, group members use the data they collected to answer their statistical question. The entire class then discusses related questions suggested by the collected data. Watch the segment after you have completed Part A.

What additional questions would you ask based on this group’s data?

You can find this segment on the session video approximately 8 minutes and 11 seconds after the Annenberg Media logo.

### Write and Reflect

**Problem A1**

What do you think of when you hear the word *statistics?*

**Problem A2**

Think of a general question that could be answered with statistics. Now think carefully about the four steps listed above. How would you carry out each step in order to answer your question? Be as specific as possible.