Overview

• In this in-class activity, students will describe the distribution of a quantitative variable based on what they observe from a graphical display, specifically a histogram.
• This activity builds upon previous activities about visualizing distributions of quantitative data and will prepare students for the next activity where they will use the features to compare distributions from different populations.
• [S3, V3, O3, V1, C3, S4, O4, V4, C5, C2  ] ← Link to EBTP descriptions 

Prerequisite assumptions

Students should be able to do each of the following after completing the What to Know assignment.

• Use technology to make a histogram of a quantitative variable.
• Use a histogram to answer questions about a distribution of a quantitative variable.
• Describe the shape of a distribution.
• Describe the center and spread of a distribution.
• Identify if there are outliers in the distribution.
• Match the description of a distribution to the graphical display.

Intended goals for this activity

After completing this activity, students should understand that common statistical language can  be used to describe a distribution based on what is observed from a graphical display, including shape, center, spread, and the presence of outliers. They should also understand that the range can be a misleading representation of spread for distributions that are skewed and/or contain outliers. They should be able to use the language of statistics to describe distributions and identify an appropriate representation of spread based on a distribution’s shape and the presence of outliers.

Synchronous Delivery and Activity Flow

The sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.

Frame the activity (3 minutes)

• Start by having a few students share responses to the opening question after discussing in pairs.  S3
• Depending on the year in school for students in your course, you may want to briefly explain what course evaluations are, how they’re administered at your institution, and how instructors may use them. V3
• Transition to the activity by briefly discussing the Objectives for the activity.

Activity Flow (18 minutes)

• Give students a few minutes to process the information displayed after the objective before starting Question 2. O3
• Have students work in pairs or groups to complete the activity. V1
• Listen to a few groups as they discuss Question 2 . If students are having difficulty with this question, bring the class back together to discuss this question as a group. The idea is just for students to think about why one variable may be more useful than another for an analysis goal. C3
• Technology
  • There is no new technology in this activity. Students will be using the Describing and Exploring Quantitative Variables tool at https://dcmathpathways.shinyapps.io/EDA_quantitative/.
• Question 4
  • Students are going to wonder about why there is a bin from 100 to 105. This is a good place to remind them that the last bin includes 100% completion. Ask students:
    • “Does it make sense for a completion rate to be >100%? Why or why not?”
    • “What is the only possible completion rate that would be counted in the last bin?”
  • If needed extend questions to other bins: “To which bin would a 95% completion rate belong?
  • This question is meant to reinforce the concepts from In-Class Activity 3.C and make sure students understand how to read a histogram. Once groups have had a few minutes to work on this question, you can use polling or ask some randomly-selected groups to share their responses to assess the class’s understanding. C3
• Question 7
  • This question asks students to consider why it’s important to include the description of the distribution even if the graphical display is available. You can ask a few groups about their responses as you walk around the room. You can have some groups share their responses during the wrap-up at the end of the activity. S4
• Questions 8 – 12
  • These questions guide students through the features of a distribution. The bottom of the digital page includes a guide to each characteristic, shape, center, spread, and outliers, that students can refer to as needed. These features are introduced in the preview assignment, so you can use the results from that assignment to gauge whether the class requires additional instruction on these concepts. O4
  • Students may be tempted to consider every peak as they describe the shape of the distribution. Ask students to think about using their fingers or pencils to roughly outline the top of the distribution. The number of peaks is the number of times their fingers/pencils move upward.
  • Guiding Questions for Question 12:
    • Ask students how the spread of the distribution changes if they don’t include the course with a completion rate close to 10%.
    • Based on their responses, do they think the range is an accurate representation of the spread of the distribution?
• Question 13 – 19
  • Have each person in the group focus on one variable and then share their results with the group. V4
  • When using the data analysis tool, the minimum and maximum values will be displayed in the output. It is hard to discern the maximum and minimum from the histogram.
  • Make note of groups with particularly interesting results and/or discussions, and you can start with these groups in the wrap-up.
  • It may be challenging for students to specify the shape of the distribution of age. Time permitting, discuss this distribution during the wrap-up.

Wrap-up/transition (5 minutes)

• Close the activity by having a few groups share their responses about why it is useful to have a written/verbal description of the distribution along with the graphical display. C5
• Time permitting, ask the groups you previously identified to share their responses about the distributions in Question 13-19, starting with age. S4
• Have students refer back to the Objectives for the activity and identify ones they recognized completing. S2, C4, O2
• Assign the homework or Practice and any What to Know pages for the Forming Connections activities you plan to complete in the next class meeting. C2