Selecting Measures of Center and Variability

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Objective

SWBAT: • Define and calculate the mean, median, mode, range, interquartile range, and mean absolute deviation. • Choose a measure of center and variability to represent a data set and justify those choices.

Big Idea

What are the pros and cons of each measure of center? What are the pros and cons of each measure of variability? Students choose measures of center and variability to represent a data set and justify their choices.

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 pictograph in order to answer questions. Each edition of Scholastic News  typically includes a graph at the end each edition.

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

Advantages and Disadvantages

5 minutes

I have students brainstorm pros and cons independently.  If they struggle, I encourage students to look at their notes from this unit.  As students are working, I walk around and monitor student behavior and progress.

Notes: Measures of Center and Variability

6 minutes

I review the notes with students.  I want students to understand how outliers affect the mean, but not the median or the mode.  I want students to understand how the interquartile range is more specific than the range, since it shows the range of the middle 50 % of the data.  This means that it is not affected by outliers.  I want students to understand that the MAD is more specific than the range and the interquartile range since it shows how the values vary within a data set.

Calculating and Selecting

25 minutes

Notes:

  • I Create Heterogeneous Groups of 3-4 for this part of the lesson.
  • I give each group a Group Work Rubric.  I use it to record the effort and behavior of each group member.
  • One option is to give students laptops and have them use Microsoft Excel to calculate the measures of center and variability.

I explain the task to students.  Not only do they need to calculate the measures, but they need to then select which measure they think best represents the data set.  Students are engaging in MP2: Reason abstractly and quantitatively and MP6: Attend to precision.

As students work, I walk around and monitor student behavior and progress.  If students struggle to complete a step, I tell them to look at their notes from the previous lesson and ask their group members.

When students start selecting their measures, I may ask them the following questions:

  • What does that measure show?
  • Why do you think that measure best represents this data set?
  • Why don’t you think that the ______________ best represents this data set?

Closure

7 minutes

I ask students to share out their calculations and their selections of center and variability.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.  Some students may share that Data Set B has an outlier, therefore they should pick the mode or the median as the measure of center.  Other students may share that that Data Set A has the same value for the median and mean.  I make sure that students justify their choices using information from the data set.

Instead of giving a Ticket to go, I collect student work.