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

# Statistics As Problem Solving

## Consider statistics as a problem-solving process and examine its four components: asking questions, collecting appropriate data, analyzing the data, and interpreting the results. This session investigates the nature of data and its potential sources of variation. Variables, bias, and random sampling are introduced.

### In This Session

**Part A:** A Problem-Solving Process

**Part B:** Data Measurement and Variation

**Part C:** Bias in Measurement

**Part D:** Bias in Sampling

**Homework**

Statistics is a problem-solving process that seeks answers to questions through data. In this session, we begin to explore the problem-solving process of statistics and to investigate how data vary. This process typically has four components:

- Ask a Question
- Collect Appropriate Data
- Analyze the Data
- Interpret the Results

### Learning Objectives

In this session, you will learn the following:

- Statistics is a problem-solving process with four components.
- Data consist of measurements of a particular variable.
- There are two types of variables — quantitative and qualitative.
- There are many sources of variation in data, including random error and bias.

### Key Terms

### Notes

Many teachers focus solely on the third component of our four-step process for statistical investigations: data analysis. But to properly understand your data, you need to do more than simply examine them. Specifically, there are four things you should consider:

A statistics problem typically contains four integral components:

- Formulation of a statistical question
- The nature of data
- Particular ways to examine data
- Types of interpretations

These four elements serve as the foundation of all the activities in this course. The activities in Part B of this session begin with a question (or questions) and then focus on the nature of data. Each activity emphasizes three points:

- Data consist of measurements of a particular variable.
- There is variation in data.
- There are many potential sources of this variation.

Two questions recur throughout this session: Why are there differences (i.e., variation) in our measurements? What is the source of this variation?

Parts C and D look at two kinds of “bias” in data. Part C uses an Interactive Activity to examine how measurement bias might arise. Part D uses an Interactive Activity that demonstrates how bias can occur in sample selection by looking at the difference between human selection and random selection.

**Materials Needed:**

- foot-long rulers
- yardsticks
- tape measures
- meter sticks
- metric rulers

The following materials are needed for those choosing to do hands-on activities:

- up to 32 pennies
- metric scales that are accurate to 1/100 of a gram
- a stopwatch or watch with a second hand
- five boxes of raisins