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 explainhow 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

Launch Partner

Agenda

7

1) Using cubes, make stacks like the ones shown below.

Arlene Paul 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?

Arlene Paul 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?

Arlene Paul Leo Al Joseph Mia

Mean = 4 letters

Launch Vocabulary

Agenda

10

The mean of a set of data is:

Arlene Paul Leo 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

Miriam Luis 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 group’s 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 Wolfe schlegelstein hausenberger dorffvoraltern waren gewissenhaft schaferswessen schafewaren wohlgepflege und sorgfaltigkeit beschutzen von angreifen durch ihrraubgierigfeinde welche voraltern zwolftausend jahres vorandieerscheinen wander ersteer dem enschderraumschiff gebrauchlicht als sein ursprung von kraftgestart sein lange fahrt hinzwischen sternartigraum auf der suchenach diestern welche gehabt bewohnbar planeten kreise drehen sich und wohin der neurasse von verstandigmen schlichkeit konnte fortplanzen und sicher freuen anlebens langlich freude und ruhe mit nicht ein furcht vor angreifen von anderer intelligent geschopfs von hinzwischen sternartigraum, Senior

Explore Small Group

Agenda

15

What happens if you don’t 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 Mean Notes

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 1 2 3 4 5 6

Mean = 4 letters

1

32

6

45

12

123

123

1234

123456

6 + 4 + 3 + 2 + 6 + 3 = 24

24 6 = 4÷246 = 4

Explore Notes

Agenda

17

Miriam Luis Ben

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.

1 2 3

123

123456

6 + 4 + 3 = 13

1234

13 ÷ 3

133

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 student’s name

2. Divide the sum by the number of students in our class

Calculate

Explore Think-Pair-Share

19

Agenda

What if Wolfe + 585 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 Wolfe schlegelstein hausenberger dorffvoraltern waren gewissenhaft schaferswessen schafewaren wohlgepflege und sorgfaltigkeit beschutzen von angreifen durch ihrraubgierigfeinde welche voraltern zwolftausend jahres vorandieerscheinen wander ersteer dem enschderraumschiff gebrauchlicht als sein ursprung von kraftgestart sein lange fahrt hinzwischen sternartigraum auf der suchenach diestern welche gehabt bewohnbar planeten kreise drehen sich und wohin der neurasse von verstandigmen schlichkeit konnte fortplanzen und sicher freuen anlebens langlich freude und ruhe mit nicht ein furcht vor angreifen von anderer intelligent geschopfs von hinzwischen sternartigraum, 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-Worksheet2-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