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# Data Clusters and Distributions

### Collection Developed by:

Collection Credits

### Collection Funded by:

Funding for the VITAL/Ready to Teach collection was secured through the United States Department of Education under the Ready to Teach Program.

## Resources for this Lesson:

Connections

Everyday Math (2004)
Teacher Lesson Guide, pp. 98- 102, 115-119
Student Reference, pp. 68, 262
Math Journal, pp. 35, 42-43
Math Master, p. 242, 246

Investigations/Scott Foresman (2006)
The Shape of the Data, all Investigations

Standards

to:

Not yet reviewed.

### Overview

In this activity, students learn some of the pitfalls of doing surveys. They also learn to examine the shape of data, including data clusters, the range and typical values. This Cyberchase activity is motivated by a video segment in which the CyberSquad searches for Hacker's castle based on a survey of where town residents have last seen him.

3-6

1 hour

### Media Resources

Using Data Clusters to Find Hacker QuickTime Video

### Part I: Learning Activity

1. Tell the students that the CyberSquad is trying to locate Hacker's castle, where Dr. Marbles is hidden. In Castleblanca, there are too many castles to check, so the CyberSquad conducts a survey asking people to put a mark on a map where they have seen a tall man with a pointy chin and cape. Based on the data, they find Dracula not Hacker.

2. Tell the students that they will see a video segment in which the CyberSquad tries to figure out how to find Hacker instead of Dracula.

3. Show the Using Data Clusters to Find Hacker QuickTime Video, and ask students to keep track of as many things as they can, which can make one's data set lead to the wrong predictions or conclusions.

4. Discuss the students' ideas.

5. Distribute the Handout: "What's Typical, Based on the Shape of Data Charts?".

6. Ask students to examine the data collected by Inez and Matt and to answer the questions.

7. Discuss their answers, noting that the two data sets differ only by one inch, suggesting perhaps that one kid measured the band members with their shoes on and one kid measured them with their shoes off. This is a systematic error in data collection.

### Part II: Assessment

Assessment: Level A (proficiency): Students are asked to examine a table of data showing the average number of hours of sleep for males and females in different age groups, and to identify the range, mode, and some other characteristics of the data set.

Assessment: Level B (above proficiency): Students are asked to examine a scatter plot of data showing records of the speed of cars and the time of day they were recorded along a certain stretch of road, to identify clusters of data, and to decide when it would be best to set up a speed trap.