<p> Topic: Variability Lesson 1: Activity 1</p><p>How big is your head?1</p><p>Part I</p><p>1. With a partner, plan a method to measure the circumference of each of your heads. What decisions did you make in doing this?</p><p>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.</p><p>Your head circumference: ______</p><p>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.</p><p>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.</p><p>Body Data Collection Box</p><p>. 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) : ______</p><p>Record each of the body measurements from the Body Data Collection Box into Excel on the Instructor’s computer.</p><p>1 Please note the possible student answer may not, in some cases, be IDEAL student answers.</p><p>1 Topic: Variability Lesson 1: Activity 1</p><p>Part II: Analyzing the head sizes for students in this class.</p><p>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. </p><p>1. What is the approximate shape of the Stem and leaf? Explain.</p><p>2. Are there clusters and gaps or unusual data values (i.e., an outlier in the data)? Explain.</p><p>3. Can you determine why they are unusual? Are they legitimate values?</p><p>4. Choose two numbers that seem reasonable for completing the following sentence. (Note: There is more than one reasonable set of choices.)</p><p>The typical head circumference is about _____cm give or take about _____cm.</p><p>5. Offer possible reasons for the variability in the measurements of students’ head circumferences. </p><p>2 Topic: Variability Lesson 1: Activity 1</p><p>6. Could the variability be reduced? Explain.</p><p>Part III: Analyzing the measurements for one student’s head size</p><p>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.</p><p>1. Describe this graph in terms of shape, center and spread.</p><p>2. How does this graph resemble or differ from the first one?</p><p>3. Offer possible reasons for the variability in these measurements? </p><p>4. Are there ways to reduce this variability? Explain.</p><p>3 Topic: Variability Lesson 1: Activity 1</p><p>Things to Consider</p><p>Think about the variability for the two sets of measurements.</p><p>. How are they different? </p><p>. When might we expect and even want variability? </p><p>. When is variability a type of error? </p><p>4 Topic: Variability Lesson 1: Activity 1</p><p>Reference</p><p>Garfield, J., Zieffler, A., & Lane-Getaz, S. (2005). EPSY 3264 Course Packet, University of Minnesota, Minneapolis, MN. </p><p>5</p>