# Average

## Overview

In general, we find that students tend to use average interchangeably along with words like "typical", which causes them to not always understand when average is being used in a strict mathematical sense. Research shows that this confusion is very frequently not resolved even after a student has completed an introductory course.

## Student Notions

When presented with a prompt such as: "A variable is measured and the value observed is determined to be an average value for that variable. What does average mean in this context?", student responses have been summarized as including one or more of the following notions (in this case, categories are not exclusive):

• Mean
• Median, including a description without using the term "median"
• Mode, including a description without using the actual word "mode"
• Normal
• In a range or interval
• Confidence Interval
• Similar, the same, like others
• Central tendency
• Other: Normal Curve/Distribution, Standard Deviation, Sum, Not Skewed

In addition, students took a standardized exam in which they were asked to compare two dot plots and assess whether the average for one group was lower than for the other and by how much.

The following chart shows the distribution of student responses between those exposed to HILT activities focus on Average and those who were not:

## Activities

The following HILT activities have been designed to address student misconceptions regarding "Average" and have research that suggests they improve student learning:

 Is Average Normal? Why Be Normal?