What is the Shape of the Data and What Can We Infer?

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SWBAT compare the shape of histograms, box plots, and dot plots using a set of data.

Big Idea

For students to be able visualize the different shapes of data and match box plots and histograms of the same distribution.

Warm Up

15 minutes

I begin this lesson by having students open their computers, and attempt matching histograms to box and whisker plots in this Online Activity.  The purpose of this lesson is for students understand the shape of different distributions of data represented by different types of graphs.

By the end of this lesson, students should be able to compare and match different graphs that represent the same data set.  If they are not able to match the graphs correctly, they should be able to explain why.

Students should pay attention to the location of the median, Quartile One, and Quartile Three when matching the graphs by shape.  If the data is right skewed, the third quartile is further away from the median.  If the data is left skewed, the first quartile is further from the median.

Students may hit the hint button for clues if they have difficulty.  Allow students about 10 minutes to explore this activity on their own before moving on to the lesson.  Allow table partners to assist those that are struggling, explaining how they are matching the graphs.

I do not give students a certain number of data sets to complete.  Students need to hit new data set to continue to get three new problems.  Students should continue to work until the end of the 10 minutes.

Power Point

20 minutes

In this Power Point, I introduce students to all of the shapes of a distribution and the vocabulary used to name them.  I want students to become comfortable describing the shape of a distribution when working with different graphs.  Students will come to find out that the Shape of the Data is related to the Center and Spread as well.  

In the first part of the Power Point, I project the slides on the screen in front of the class, and we discuss how to describe each shape. We begin by looking at the different shapes of histograms, and box plots separately. Then we begin comparing dot plots, box plots, and histograms of the same shape.

Finally, I have students work with their table Partner on a Cooperative Activity.  I cut out the cards from the following website:


Students work together to match a Statistic Card to a Box Plot to a Histogram. I post the final slide of the Power Point on the projector to provide students instructions as they are working.  It is important for students to provide reasoning (MP2) as they take turns matching each card.  It is also important for their table Partner to agree or disagree with their match, and also provide reasoning.(MP3)

Exit Slip

15 minutes

With about 10 minutes remaining in the period, I hand each student an Exit Slip.  In the Exit Slip, I provide the students with a set of data about the amount of sugar in grams that is in one serving of popular cereals that we eat.  I want each student to work the Exit Slip individually to provide me with a quick formative assessment of their ability to explain a distribution of data using Center, Spread, and Shape.

  • In number one, students should graph either a Dot Plot, a Histogram, or a Box Plot on their graphing calculator, and provide a sketch of the graph.  


  • Students should explain in number two that the graph is skewed right because most of the data is clustered on the left.


  • Finally, students should infer that the number of grams of sugar in one serving of cereal that we eat varies.  Therefore, a consumer should read labels.  However, this data shows that most of the cereal we eat has under 10 grams of sugar per serving.  Since the data is skewed right, that means that most of the cereals have a low amount of sugar per serving.