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

# Data Organization and Representation Part A: Patterns in Variation (10 minutes)

To answer a statistical question, we collect data, which consist of measurements of a variable. When the measurements we collect differ from each other, variation exists. We can examine this variation in several ways to find interesting answers to the statistical questions we pose.

For example, we can look at the distribution of a data set — the different values and how often each occurs — to draw out informative patterns in the variation. Tabular and graphical representations of the data can help to display these patterns.

In the video segment below, Professor Kader and the participants examine the distribution of a data set to help explain an intriguing aspect of the variation they find. Professor Kader also introduces the uses of graphical and tabular representations. See Note 2.

**Video Segment **

In Problem H2 of Session 1, you looked at the mint marks of 100 Jefferson nickels. Then you answered a series of questions about those coins. In this video segment, the onscreen participants examine the distribution of coins to come up with a hypothesis about where the coins without mint marks (N) were minted. After you watch the video segment, reflect on the questions below.

You can find this segment on the session video approximately 8 minutes and 30 seconds after the Annenberg Media logo. The second part of this segment begins approximately 10 minutes and 3 seconds after the Annenberg Media logo.

**Problem A1**

Did you arrive at the same conclusions about where the coins were minted as the onscreen participants did? Was your reasoning similar or different from theirs?

### Notes

**Note 2**

If you’re working with a group, you may want to organize a coin activity based on Problem H2 from Session 1 before watching the video segment. Here’s how the activity can be organized:

Label the corners of a large square poster board with the letters P (for Philadelphia), D (for Denver), S (for San Francisco), and N (for none). Separate 100 nickels according to mint mark (using magnifying glasses, if needed), and place them on the corner of the poster board corresponding to their mint location. Discuss the following question:

- Based on what you see, what can you say about the way the coins are distributed among the four different mint marks?

Statisticians find it useful to think in fractional terms, i.e., proportions or percentages. In order to start thinking about the coin data in fractional terms, cross two pieces of string to divide the poster board into four sections (one for each mint location). Adjusting the strings to keep the coins from each of the four mint marks separate, slide the coins to form a circle. This will result in a pie chart. Discuss the following questions:

- Based on what you see in the pie chart, what can you say about the way the coins are distributed among the four different mint marks? Specifically, what fraction of the total would you guess is represented by each group?
- Which location has the most coins? Why do you think this location is the most common?
- Which location has the least coins? Why do you think this location is the least common?

Watch the video segment, and compare your hypotheses with those of the online participants.