Using the Mean as a Measure of Center Lesson 3 1

Warm Up OBJECTIVE: SWBAT understand the mean as a number that evens out or balances a distribution and recognize how the mean reacts to changes made to a data set. Language Objective: SWBAT write about what happens to the mean when a data set changes. Agenda 2 The line plot below shows the number of hits made by each of 10 players on a baseball team during batting practice. 1.What was the median number of hits made by the players? Show or explain how you got your answer. 2. Two additional players arrived at practice. The median number of hits increased. What could be the number of hits made by each of the two additional players? Show or explain how you got your answer. Median: The middle number in an ordered set of data 10.5 hits 12 hits and 13 hits

Launch – Review Turn and Talk (30 sec) number of toppings students like on their pizzas 3 When we analyze data, what are we looking for? Center Spread Shape Median Mean Agenda Today!

Launch Agenda 4 Six students in a middle-school class make a stack of cubes to show the number of letters in his or her name. You can see from the stacks that the six names vary in length. Arlene Paul Leo Al Joseph Mia

Launch - Review Agenda 5 What is the median name length? Arlene Paul Leo Al Joseph Remember to order the data from least to greatest! Mia

Launch - Review Agenda 6 What is the median name length? Arlene Paul Leo Al Joseph Median = 3.5 letters Mia

LaunchPartner Agenda 7 1) Using cubes, make stacks like the ones shown below. ArlenePaul Leo Al Joseph 2) Make the 6 stacks all the same height by moving the cubes around. Mia

Launch Whole Class Agenda 8 How many cubes should be in each stack so that the heights are all the same? ArlenePaul Leo Al Joseph Mia

Launch Think-Pair-Share Agenda 9 The stack height that you found represents the mean number of letters in the students names. How might you explain what the mean of a data set is? ArlenePaulLeo Al Joseph Mia Mean = 4 letters

Launch Vocabulary Agenda 10 The mean of a set of data is: ArlenePaulLeo Al Joseph Mia the balance point or average of a data set. It represents the value that each data point would take on if the total of the data values were redistributed equally.

Launch Turn and talk (30 secs) Agenda 11 Imagine the image below contains glasses of water. Explain to a friend how to find the mean amount of water.

Launch Notes Agenda 12 MiriamLuis Ben What is the mean number of letters in the set of data below? How can this cube be distributed evenly?

Launch: First Names Small Group Agenda 13 1) Create a stack of cubes to represent the letters in your own first name. 2) Line up your stack with those of your group members. 3) Find the mean number of letters in your groups set of data by redistributing the cubes to make the stacks all the same height.

Explore Agenda 14 So I need to have cubes in my pocket every time I need to find the mean? Yikes! What if Wolfe+585 joined my group! He has 590 letters in his name! That is a lot of cubes to redistribute! Adolph Blaine Charles David Earl Frederick Gerald Hubert Irvin John Kenneth Lloyd Martin Nero Oliver Paul Quincy Randolph Sherman Thomas Uncas Victor William Xerxes Yancy Zeus Wolfe­schlegelstein­hausenberger­dorffvoraltern­ waren­gewissenhaft­schaferswessen­schafewaren­wohlgepflege­und­sorgfaltigkeit­beschutzen­von­angreifen­durch­ ihrraubgierigfeinde­welche­voraltern­zwolftausend­jahres­vorandieerscheinen­wander­ersteer­dem­enschderraumschiff­ gebrauchlicht­als­sein­ursprung­von­kraftgestart­sein­lange­fahrt­hinzwischen­sternartigraum­auf­der­suchenach­diestern­ welche­gehabt­bewohnbar­planeten­kreise­drehen­sich­und­wohin­der­neurasse­von­verstandigmen­schlichkeit­konnte­ fortplanzen­und­sicher­freuen­anlebens­langlich­freude­und­ruhe­mit­nicht­ein­furcht­vor­angreifen­von­anderer­intelligent­ geschopfs­von­hinzwischen­sternartigraum, Senior

Explore Small Group Agenda 15 What happens if you dont have cubes and you are asked to find the mean? How else could you find the mean? Hints! -Count how many stacks you have at your table. -Count how many cubes you have altogether.

Explore: How to Find the MeanNotes Agenda 16 1) Add up all of the values in the data set. Arlene Paul Leo Al Joseph 2) Divide the sum by how many values there are in the data set. Mia Mean = 4 letters = = 4 ÷ 24 6 = 4

Explore Notes Agenda 17 MiriamLuisBen 1) Add up all of the values in the data set. 2) Divide the sum by how many values there are in the data set = ÷3 3

Explore – Class Challenge! Whole Class Agenda 18 How would we calculate the mean number of letters in students names in our class? 1. Add up the number of letters in every students name 2. Divide the sum by the number of students in our class Calculate

Explore Think-Pair-Share 19 Agenda What if Wolfe really did join our class?! How would that piece of data affect the average number of letters in students names? Adolph Blaine Charles David Earl Frederick Gerald Hubert Irvin John Kenneth Lloyd Martin Nero Oliver Paul Quincy Randolph Sherman Thomas Uncas Victor William Xerxes Yancy Zeus Wolfe­schlegelstein­hausenberger­dorffvoraltern­waren­ gewissenhaft­schaferswessen­schafewaren­wohlgepflege­und­sorgfaltigkeit­beschutzen­ von­angreifen­durch­ihrraubgierigfeinde­welche­voraltern­zwolftausend­jahres­ vorandieerscheinen­wander­ersteer­dem­enschderraumschiff­gebrauchlicht­als­sein­ ursprung­von­kraftgestart­sein­lange­fahrt­hinzwischen­sternartigraum­auf­der­suchenach­ diestern­welche­gehabt­bewohnbar­planeten­kreise­drehen­sich­und­wohin­der­neurasse­ von­verstandigmen­schlichkeit­konnte­fortplanzen­und­sicher­freuen­anlebens­langlich­ freude­und­ruhe­mit­nicht­ein­furcht­vor­angreifen­von­anderer­intelligent­geschopfs­von­ hinzwischen­sternartigraum, Senior Calculate

20 Agenda What if Justin joined our class instead of Wolfe + 585?! How would that affect the average number of letters in students names? Explore Think-Pair-Share Calculate

Summary Think-Pair-Share 21 Agenda Previously we discussed how the median reacts to changes made to a data set. How does the mean react to changes made to a data set? Be prepared to explain your thinking.

Practice 22 Part 1 - (10 Min) Work independently and check in with a partner to complete your class work. 1-Worksheet 2-Share Out In 10 minutes you will be asked to stop and share your answers! Click on the timer! Agenda

Practice – Student Share Out 23 Part 2 – (5 Min) Students share out work. Classwork Questions Agenda