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Instructor Overview

In this lesson, students are given criteria about measures of center, and they must create line plots for data that meet the criteria. Students also explore the effect on the median and the mean when values are added to a data set.

Students use a tool that shows a line plot where measures of center are shown. Students manipulate the graph and observe how the measures are affected. Students explore how well each measure describes the data and discover that the mean is affected more by extreme values than the mode or median. The mathematical definitions for measures of center and spread are formalized.

Key Concepts

Students use the Line Plot with Stats interactive to develop a greater understanding of the measures of center. Here are a few of the things students may discover:

  • The mean and the median do not have to be data points.
  • The mean is affected by extreme values, while the median is not.
  • Adding values above the mean increases the mean. Adding values below the mean decreases the mean.
  • You can add values above and below the mean without changing the mean, as long as those points are “balanced.”
  • Adding values above the median may or may not increase the median. Adding values below the median may or may not decrease the median.
  • Adding equal numbers of points above and below the median does not change the median.
  • The measures of center can be related in any number of ways. For example, the mean can be greater than the median, the median can be greater than the mean, and the mode can be greater than or less than either of these measures.

Note: In other courses, students will learn that a set of data may have more than one mode. That will not be the case in this lesson.

Goals and Learning Objectives

  • Explore how changing the data in a line plot affects the measures of center (mean, median).
  • Understand that the mean is affected by outliers more than the median is.
  • Create line plots that fit criteria for given measures of center.