Deciding Which Measure of Center to Use Lesson 8

Warm Up Number of Pets Per Household OBJECTIVE: Students will be able to determine which measure of center is best according to the shape and context of the data.: Language Objective: Students will be able to define and differentiate between the words nominal and ordinal. 1. Can you estimate what the “center” of the data is without doing any calculations? Number of Pets Per Household 2. Find the mean, median, and mode of the data set. (5 Min) 0-5 In-Class Notes Ask students to share aloud their approximations before they calculate the mean, median, and mode. Once they are done with problem 2, ask the students which they think is the “best” measure of center. Sometimes they already have a firm understanding of center, and when to use different techniques. Preparation Notes You may need to remind students the techniques to find mean, median, and mode. If students are having trouble seeing, it may be a good idea to print out the line plot. 3. Which of the three is closest to your approximation? Agenda

Launch Vocabulary 1. Nominal: A nominal data set cannot be put in order. An example of a nominal data set would be a list of favorite colors for everyone in the class. 2. Ordinal: An ordinal data set can be put in order from least to greatest. An example of an ordinal data set would be a tally of how many students slept a certain number of hours last night. (Time on this slide – 2 min) 6 - 8 In-Class Notes An easy way to remember this is the word “Ordinal” starts the same as the word “Order.” Make sure to point this out to you students. If time permits, ask the students if they can come up with any examples of their own. Have students copy these vocabulary words into their notebooks, along with definitions. Preparation Notes It might be a good idea to have a few other examples in mind in case students ask you questions. Agenda

(Wait time: 30 seconds for each question) Launch (Wait time: 30 seconds for each question) Can you determine whether the following data sets are nominal or ordinal? A graph with everyone’s favorite food on it? Nominal! …Why? A table with the height of each of your classmates? Ordinal!… Why? A bar graph with how many middle schools each city in MA has? Nominal!…Why? A number line with the ages of each of the presidents when they first took office? (2 min) 8 – 10 In-Class Notes Give students 30 seconds each for the questions. Accommodation: Hand out a piece of paper for students that would like more time to look at the questions. Use calling sticks to have students share their answers For Problem 4 - Make sure students realize a number line can only be used with ordinal data sets. Preparation Notes Have the students explain WHY they chose the answer they did. This will help some students who were confused by the definition of ordinal and nominal. This will help them better determine what the best measure of center is later on. Ordinal!… Why? A survey that asks the time of TV watched per day of 200 high school students? Ordinal! … Why? Agenda

Can you find the mean and the median for a nominal data set? Launch (Wait time: 1 minute) Open Question: Can you find the mean and the median for a nominal data set? Why or why not? (2 min) 10 – 12 In-Class Notes The answer for this questions is no, but the important part of the questions is the “why or why not.” Urge the students to answer this part, not just yes or no. Agenda

In 10 minutes you will be asked to stop and present! Explore Work with your group. You will see a data set, and the goal is to find the best measure of center. You will get a worksheet and a calculator. You should: Represent the data in a graph Find the Mean, Median, and Mode (if possible) Determine which is the best to use based on the data! Click on the timer! 1-Partners 2-Share Out 3-Discussion Online timer link on slide – (8 min) (10-20) In-Class Notes Pass out “Explore” Classwork, Calculator. Focus on strategies and help struggling pairs recall previous techniques click the timer to give a 10 minute countdown. In 10 minutes you will be asked to stop and present! Agenda

Explore While working with your group remember: 1. Everyone Contributes! 2. Answer each part of the question! 3. Ask questions if you get stuck! (1 min) 20-21 In-Class Notes Make sure everyone is paying attention to this before the groups actually form. It might be a good idea to see this on the board while they are working. You can also obtain the timer from the clock on the right hand side. Preparation Notes There is no pre-assigned way to form the groups, since class sizes and techniques always differ; have fun with this and make the groups however you prefer! Agenda

Explore – Student Share Out Discussion - (5 Min Each) Students share out work. Fill in your sheet as you hear each group present! (20 min) 21 – 41 In-Class Notes Pass out the audience worksheet so the students who are listening are also participating. Tell each group they have 5 minutes to present their scenario. Preparation Notes This share out is an essential part of the lesson, and students will see how each data set can be approached differently depending on the person. The most important thing to stress is that the reason you picked the measure of center is explained. If there is not enough time to present in this class, skip to the “practice questions” and have students present and do the exit ticket next class. This gives them more time to talk in front of the class and answer questions as well. Classwork Questions Agenda

Explore Guidelines for presenting: 1. Explain your scenario 2. Describe what type of visual display you created. 3. Explain what measure of center the group decided was best, and state WHY you chose this. (20 min) 21 – 41 In-Class Notes If the students go over each problem from the exploration and answer it, this should be enough to satisfy the three guidelines for presenting. Remind students that they will each have a certain time frame for their presentations. (recommended 5 minutes) Agenda