# Lesson 10

The Effect of Extremes

### Lesson Narrative

The mathematical purpose of this lesson is to recognize a relationship between the shape of a distribution and the mean and median. Students will use dot plots to investigate this relationship. Earlier in this unit, students created data displays so that the shape of the distribution is clear. This lesson connects to upcoming work because students will use the shape of the distribution and measures of center to make decisions about how to summarize data.

In this lesson, students begin by using aspects of mathematical modeling (MP4) to select appropriate variables to compare. In another activity, students make use of structure (MP7) and appropriate tools (MP5) to construct dot plots of data that have prescribed measures of center.

One of the activities in this lesson works best when each student has access to technology that will easily compute measures of center to produce dot plots or histograms because it will help students focus on understanding the relationship between extreme values and the measure of center without distracting with lengthy computations.

### Learning Goals

Teacher Facing

• Recognize the relationship between mean and median based on the shape of the distribution.
• Understand the effects of extreme values on measures of center.

### Student Facing

• Let’s see how statistics change with the data.

### Required Preparation

Acquire devices that can run GeoGebra (recommended) or other spreadsheet technology. It is ideal if each student has their own device. (A GeoGebra Spreadsheet is available under Math Tools.)

Internet-enabled devices are required for the digital version of the activity Separated by Skew.

### Student Facing

• I can describe how an extreme value will affect the mean and median.
• I can use the shape of a distribution to compare the mean and median.