Choosing the Best Measure of Center

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Objective

SWBAT: • Calculate the mode, mean, median, and range of a data set. • Define and identify outliers in a data set. • Determine which measure of center best represents a given situation.

Big Idea

Does the mean, median, or mode best represent this data set? Students calculate the measures of center and consider outliers and context in order to choose the best measure of center.

Do Now

7 minutes

See my Do Now in my Strategy folder that explains my beginning of class routines.

Often, I create do nows that have problems that connect to the task that students will be working on that day.  Today I want students to analyze a circle graph in order to answer questions. Each edition of Scholastic Action  typically includes a graph on its back page.

I ask for students to share their thinking.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Problem

7 minutes

I ask students to use the skills we have developed in this unit to answer the questions.  Students participate in a Think Write Pair Share.  I quickly review the answers to problem 1.  I want to ensure that students are able to accurately calculate the mean, median, mode, and range.

 

3 Corners

5 minutes

Note:

  • Before this lesson, I place 3 signs in 3 corners of my room that read median, mean, and mode.

I review the expectations for moving around the room.  I also encourage students to go to their corner and try not to be persuaded by what other people are doing.  I am interested in different ideas.

I give students a minute to talk about why they are in their corner.  Then I call on students at each corner to share out their reasoning.  Students are participating in MP3: Construct viable arguments and critique the reasoning of others.

Outliers

5 minutes

We go over the notes together.  I want students to understand that an outlier greatly affects the mean, since we add up all of the values and then divide by the number of values in the set.  I also explain that depending on the situation, it may be better to choose a particular measure of center.

Practice

16 minutes

Notes:

  • Before this lesson, I use the exit tickets from the previous lesson to Create Homogeneous groups of 3-4 students. 
  • Each group also gets a Group Work Rubric.
  • I create and Post a Key.

Students work in their groups while I walk around to monitor student progress and behavior.  Students are engaging in MP2: Reason abstractly and quantitatively, MP3: Construct a viable argument and critique the reasoning of others, MP4: Model with mathematics and MP6: Attend to precision.

If students are struggling, I may ask them one or more of the following questions:

  • How do you calculate the mode/median/mean?
  • Are there any outliers? How do you know?
  • For this situation, which measure of center is the best? Why?

When students finish a page, I quickly check in with them.  If they are on track, I let them use the key to check their work and move on.  

Closure and Ticket to Go

10 minutes

I ask students to turn to problem 3 about the gymnasts.  I quickly go over the mean, median, and mode for each gymnast.  Then as ask students to share out which gymnast they would pick to compete in the state competition.  I am interested to hear why students nominated particular gymnasts.  Students are engaging in MP2: Reason abstractly and quantitatively, MP3: Construct viable arguments and critique the reasoning of others, and MP4: Model with mathematics.

I pass out the Ticket to Go and the Homework.