# Sampling Distribution of an Average: Exercises to Aid Student Understanding

#### Summary

These exercises are designed for student work in groups. Together the students grapple with the general idea of sampling distributions, specific application of the sampling distribution of an average, and along the way they must justify their steps conceptually. The activity is designed for a single class period, with nothing to turn in at the end. I typically provide an answer key at the end of class, so students know whether they understand the concepts. (Through experience, I found the in-depth student discussions to be most important. And if I required groups to turn in careful solutions, then there wasnt enough time in one class period. But, this format can be modified, so the students discuss in groups, but then turn in individual solutions the next class period. In fact, this might be even better for their learning–I just havent done it, because of the grading load.)

## Learning Goals

This activity should help solidify a specific concept: the sampling distribution of the mean. Furthermore, the students should better understand how to explain their solutions and ask questions of their methods.

## Context for Use

I use this activity shortly after I introduce the specific concept of the sampling distribution of the mean. We might have class discussion of this topic on a Monday, and then during our scheduled lab time that week, Ill use this activity. This takes an entire class period, whether that is a lab session or a classroom session. Its possible to modify the activity as a first introduction to the sampling distribution of the mean.

## Description and Teaching Materials

The teaching material needed is only the exercises themselves (3-page document). The students will also need a calculator and access to a normal-distribution table (although the activity can be modified to not include calculations).

Sampling-Distribution Exercises (Microsoft Word 2007 (.docx) 79kB Jun8 11)
## Teaching Notes and Tips

For this activity to work best, the instructor should walk around the classroom, listening to group discussions. If there are any misconceptions expressed in student discussion (which are not quickly addressed by another student), then thats a good time for the instructor to intervene with probing questions and, if needed, explanations. Also, students are sometimes unsure of how much detail to provide with the answers–they typically err on the side of less detail. Again, the instructor can ask questions to model the process the students should follow.

## Assessment

As mentioned previously, I do not require students to turn in solutions for this activity, although I think that would be the best form of assessment. (For example, have small-group discussion, but then require students to submit individual solutions.) I typically use the student discussions, my possible interventions, and the groups comparison with my solutions at the end as measures of whether the goals are met.

## References and Resources