Data Representations

5 min

Narrative

The purpose of this Warm-up is to elicit the idea that the same data can be displayed in different ways, which will be useful when students create different data displays in a later activity. While students may notice and wonder many things about these images, the comparison of the three representations and interpreting the information in each representation are the important discussion points.

This is the first Notice and Wonder activity in the course. Students are shown three statistical displays representing the same data set and are asked “What do you notice? What do you wonder?”

Students are given time to write down what they notice and wonder about the displays and then time to share their thoughts. Their responses are recorded for all to see. Often, the goal is to elicit observations and curiosities about a mathematical idea that students are about to explore. Pondering the two open questions allows students to build interest about and gain entry into an upcoming task.

This prompt gives students opportunities to see and make use of structure (MP7). Specifically, they might use the structure of the three representations, particularly the structure of the horizontal number line, to find mathematically important similarities in how the same set of data is represented.

Launch

Arrange students in groups of 2. Display the images for all to see. Ask students to think of at least one thing they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things they notice and wonder.

Student Task

The dot plot, histogram, and box plot summarize the hours of battery life for 26 cell phones that are constantly streaming video. What do you notice? What do you wonder?

<p>Dot plot from 1 to 8 by 0.5’s. battery life in hours. Beginning at 1, number of dots above each increment is 0,0,0,2,2,4,2,4,2,6,2,2,0,0,0.</p>

<p>Histogram from 1 to 8 by 1’s. battery life in hours. Beginning at 1 up to but not including 2, height of bar at each interval is 0, 2, 6, 6, 8, 3, 4, 0.</p>

<p>Boxplot from 1 to 8 by 0.5’s. battery life in hours. Whisker from 2.5 to 3.5. Box from 3.5 to 5.5 with a vertical line at 4.5. Whisker from 5.5 to 6.5.</p>

 

Sample Response

Things students may notice:

  • The box plot has a vertical line of symmetry but the histogram does not.
  • 5.5 hours is the most common battery life.
  • 2.5 hours is not very long for a cell phone to last.

Things students may wonder:

  • Is the 3 hours of battery life included in the second bar in the histogram or the first bar?
  • Why does the histogram have intervals of 1 instead of 2?
  • How do you create a box plot from data?
Activity Synthesis (Teacher Notes)

Ask students to share the things they noticed and wondered. Record and display their responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the images. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to observe what is on display and to respectfully ask for clarification, point out contradicting information, or voice any disagreement.

The goal is to help students recall different ways to represent distributions of data. Highlight the similarities between the dot plot and the histogram. Tell students that the tallest bar in the histogram is created from the two data values at 5 and the six data values at 5.5 in the dot plot, and that the final bar is created from the two data values at 6 and the two data values at 6.5 in the dot plot. If time permits, discuss questions such as

  • “Which representation(s) shows all the data values?” (The dot plot shows all the data values.)
  • “How do you create a box plot?” (You calculate the values for the five-number summary and then graph them on a number line. The first quartile, the median, and the third quartile are used for the box, and the minimum value and maximum value are used for the whiskers.)
Standards
Building On
  • 6.SP.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
  • 6.SP.B.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
Building Toward
  • HSS-ID.A.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • S-ID.1·Represent data with plots on the real number line (dot plots, histograms, and box plots).