Median, Mode, and Range

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Objective

SWBAT: • Organize data in a line plot, histogram, and stem-and-leaf plot. • Define and identify mode, range, and median. • Describe shape of data (symmetrical, skewed left or skewed right).

Big Idea

What do the median, mode, and range tell us about a set of data? Students review median, mode, and range as well as collect and display their own data using line plots, histograms, and stem-and-leaf plots.

Do Now

7 minutes

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 line graph in order to answer questions. Scholastic News  has a 5th-6th grade edition that typically includes a graph on its back page.

I ask for students to share their thinking.  I want students to realize that the y-axis is showing acres in the millions.  I want students to explain how they found their answers and what they notice from looking at the graph.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

Review: What is Statistics?

2 minutes

I have volunteers read through the steps involved in statistics. I want to quickly review these different parts before we move on in the lesson.

Develop a Question and Collect Data

5 minutes

Note:

  • Before this lesson I create a space on my whiteboard for student responses to the question.  I label and mark the axis so students can quickly place their post-its.

I ask students which question best matches what I am trying to figure out.  Students participate in Think Pair Share.  I call on students to share their thinking.  I ask students why the other questions are not the best match.  Students are engaging in MP3: Construct viable arguments and critique the reasoning of others.

I pass out the post-its and students write down the number of people living in their household.  I call students up by rows to place their post-its on the line plot.  

Displaying Our Data

13 minutes

I ask for students to define “frequency”.  I want students to realize that frequency means the number of times a value is repeated.  Most students will be familiar with line plots and frequency tables from previous grades.  If this is the case, we can work through these examples more quickly.  Students are engaging in MP4: Model with mathematics.

I introduced students to histograms in the first unit, but we have not worked with them very often.  After we read about the example, I ask students how we should label the x and y-axis.  I want students to realize that the x-axis shows the age of the people and the y-axis shows the frequency. 

I introduce the ways we can describe a data set’s distribution.  I ask students to return to the example histogram and our histogram and ask, “How can we describe the spread of the data in these two histograms?”

Stem-and-leaf plots will most likely be new to students.  Together we create a list of class sizes that are shown in the example stem-and-leaf plot.  Then we use the class data to create our own stem-and-leaf plot.

Before moving on, I ask students, “Look at the graphs we have created today. What are the advantages and disadvantages of each type of graph?”  Students participate in a Think Pair Share.  Some students may observe that stem-and-leaf plots only work when your data is numbers.  Other students may observe that histograms can take a lot of data values and create a display that is easy to read, but you don’t know all of the individual values.   

Analyzing Our Data

13 minutes

My students have been exposed to mode, median, and range in previous grades.  I ask students to use the data set to determine the meaning of the mode, median, and range.  Students participate in a Think Write Pair Share.  Some students may use their prior knowledge to answer the questions.  Other students may have an idea of the meaning, but they will need to use the examples to determine the meaning of each measure.  Students can work on the challenge questions if they finish early.

We go over the definitions of each measure together. Students work in partners to determine the median, mode, and range of our data set.  Students are engaging in MP6: Attend to precision.  I call on students to share out their findings.  I ask them which graph/table was the easiest for them to work with to determine each measure.  

Closure and Ticket to Go

10 minutes

I have students complete the Step 4 questions as a closure.  I ask students to share out their ideas.  I push students to be specific and to show how the data supports their ideas.  Students are engaging in MP2: Reason abstractly and quantitatively, MP3: Construct viable arguments and critique the reasoning of others and MP6: Attend to precision.

I pass out the Ticket to Go and the Homework.