What Does a Mean Mean

Topic: Variability Lesson 1: Activity 1

How big is your head?1

Part I

1. With a partner, plan a method to measure the circumference of each of your heads. What decisions did you make in doing this?

2. Using your measuring tape, measure each of your heads using the protocol established by your class. Record your head circumference below, and on the board.

Your head circumference: ______

Next, as a class, we will choose one person who will have their head measured by every student in the class. Record your measurement of this person’s head circumference on the board.

3. Work with a partner to obtain the other body measurements listed below. Make all measurements in centimeters. Record each of your measurements in the Body Data Collection Box.

Body Data Collection Box

. Height (with shoes on) : ______. Arm Span (from fingertip to fingertip with arms out-stretched) : ______. Kneeling Height: ______. Hand Length (from the wrist to the tip of the middle finger) : _____ . Hand Span (from the tip of the thumb to the tip of the pinkie while hand is stretched) : ______

Record each of the body measurements from the Body Data Collection Box into Excel on the Instructor’s computer.

1 Please note the possible student answer may not, in some cases, be IDEAL student answers.

1 Topic: Variability Lesson 1: Activity 1

Part II: Analyzing the head sizes for students in this class.

We will now use Excel to create a plot of students’ head sizes so that we can see and describe the distribution of head circumferences. Follow the instructions below to help you accomplish this task.

1. What is the approximate shape of the Stem and leaf? Explain.

2. Are there clusters and gaps or unusual data values (i.e., an outlier in the data)? Explain.

3. Can you determine why they are unusual? Are they legitimate values?

4. Choose two numbers that seem reasonable for completing the following sentence. (Note: There is more than one reasonable set of choices.)

The typical head circumference is about _____cm give or take about _____cm.

5. Offer possible reasons for the variability in the measurements of students’ head circumferences.

6. Could the variability be reduced? Explain.

Part III: Analyzing the measurements for one student’s head size

Now, look at the data for measurements of the student’s head circumference that everyone measured. Enter this data in Excel. Create a Stem plot of the distribution and use that graph to answer the following questions.

1. Describe this graph in terms of shape, center and spread.

2. How does this graph resemble or differ from the first one?

3. Offer possible reasons for the variability in these measurements?

4. Are there ways to reduce this variability? Explain.

Things to Consider

Think about the variability for the two sets of measurements.

. How are they different?

. When might we expect and even want variability?

. When is variability a type of error?

Reference

Garfield, J., Zieffler, A., & Lane-Getaz, S. (2005). EPSY 3264 Course Packet, University of Minnesota, Minneapolis, MN.