The Arizona STEM Acceleration Project

Human Box Plot - Part 1

Human Box Plot - Part 1

A 9 -12 grade STEM lesson

Laura Richmond

06/30/2024

Notes for teachers

This lesson is best taught with 20+ students to provide enough individual data points to create a box plot with a clear 5 number summary.

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Students will create box plots to represent class data and make observations about that data.

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They will first physically make a dot plot by using their bodies as the data points and then section themselves into four equal-sized groups (same number of students in each) to conceptualize the five number summary and understand what the box and whiskers of a box plot represent.

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Students will share general observations about the class data based on where students are standing and then focus their observations on the size of each of the four groups and how spread apart the students are in each group as an introduction to spread.

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Then, they will transfer that data to a paper version in their group. Finally, they will use GeoGebra to create a box plot.

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At the end of the lesson, students will discuss the advantages of using boxplots to understand data.

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This lesson is intended to develop conceptual understanding of a box plot before moving into comparison of two data sets using box plots.

List of Materials

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• Teacher Mood Dotplot and Box Plot
• Pre-made number line on floor:
• Painter’s Tape
• Numbered cards (1 - 10)
• Paper Plates
• Grid Chart Paper
• Rulers / Meter Sticks / Yard Sticks
• Markers
• Dot Stickers
• Vocabulary Cards/Labels
• Lower Extreme (Minimum)
• Upper Extreme (Maximum)
• Median
• Lower Quartile (Q1)
• Upper Quartile (Q3)
• Student Computers w/ GeoGebra access

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Math Standards

A1.S-ID.A Summarize, represent, and interpret data on a single count or measurement variable.

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• A1.S-ID.A.1 Represent real-value data with plots for the purpose of comparing two or more data sets.

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Preparing students for:

• A1.S-ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

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• A1.S-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of outliers if present.

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Technology Standards

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• 9-12.5.b. Students collect data or identify relevant data sets, use digital tools to analyze them, and represent data in various ways to facilitate problem-solving and decision-making.

Objectives:

• We will collect classroom data and determine the five number summary of that data.
• We will use the five number summary to represent classroom data with a box plot.
• We will use graphing technology to create a box plot.
• We will explain what each portion of the box plot represents in the context of the data.
• We will describe the benefits of using box plots to represent data.

Agenda

1. Teacher Mood Dot Plot and Box Plot (5 minutes)
2. Student Mood Dot Plot and Box Plot (15 minutes)
3. Poster Dot Plot and Box Plot (10 minutes)
4. GeoGebra Box Plot (10 minutes)
5. Class Discussion / Closure (5 minutes)
6. Ticket Out (10 minutes)

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Intro/Driving Question/Opening

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[Show a dot plot and box plot representing teacher moods (rated 1 - 10) when they first woke up that morning]

Ask:

• What do you notice about these two representations?
• What are the similarities?
• What are the differences?

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• How do you suppose data displays like this box plot help us communicate information about a group of people?

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• What might our class box plot look like in comparison? Why?

Hands-on Activity Instructions:

Human Box Plot

1. Have students rate their mood when they first woke up in the morning and write it on a paper plate along with their name. Instruct students to stand above the pre-created number line on the floor forming a line (with their plate) at the number that matches their response to the question to form a human dot plot. Take a photo to be used for reference later.
2. Ask students to identify the lowest mood rating chosen by students and the highest mood rating chosen by students. Label as the lower extreme (minimum) and upper extreme (maximum) and mark above the number line with painter’s tape.
3. Have students equally part themselves into two groups (the lower half and upper half of data). They may decide this is more easily done if they stand in a single line in numerical order. Discuss that the median splits the entire data set into two equal-sized groups that represent the lower half and upper half of the data. Identify, label, and mark the median with painter’s tape above the number line. (Discuss that it is represented by the middle data value in the set when there’s an odd number of data values. It is represented by a value that is exactly the same distance away from the two values closest to the center/middle of the data set when there’s an even number of data values.)
4. Ask the students in the lower half to equally part themselves again in the same manner as they did in the last step. Identify, label, and mark the lower quartile above the number line with painter’s tape. Discuss that the lower quartile splits the lower half of data into two equal-sized groups.
5. Ask students in the upper half to do the same in their group. Identify, label, and mark the upper quartile above the number line with painter’s tape. Discuss that the upper quartile splits the upper half of data into two equal-sized groups.
6. Ask the students to remember which group they were in (or which part of the five number summary they represented) and move out of the number line area. With painter’s tape, use the five number summary to form a box plot. Then have the students place themselves on the box plot according to their mood rating and which group they were in when sectioned off.
7. Discuss how the lower quartile, median, and upper quartile split the data into four equal-sized groups. Connect the word “quartile” to “quarter” as needed to support this idea.
8. Encourage students to share observations. Elicit responses about what it means to be in the “box” portions or the “whisker” portions of the plot. Discuss how spread apart the data values are in each section of the plot and what that means in the context of mood ratings. Focus students on explaining where 25% of responses landed, 50% responses landed, etc.

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1. Have students work in pairs or groups of 3 to reconstruct the dot plot on grid chart paper using rulers, markers, and dot stickers using the reference photo taken at the start of the human box plot activity..

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1. Above the dot plot, have students recreate the box plot you created on the floor as a class.
2. Have them identify/label the five number summary and write at least 4 observations/interpretations about the data in context. Encourage them to describe the center of the data as well as the spread if they’re ready. Provide sentence starters such as “Approximately 25% of students rated their moods between ___ and ___.”
3. Demonstrate how to create a box plot and identify key statistics using GeoGebra, having kids follow along on their computers at each step.
4. Ask students to discuss in their groups the advantages and disadvantages of using technology to create a box plot.
5. Discuss the uses of box plots and when they are most appropriate for displaying data. Include conversation about what they show really well and what they lack.

Hands-on Activity Instructions:

Poster Plot & GeoGebra

Assessment

Given another set of student data, have students make a box plot using GeoGebra.

Have them answer the following questions:

1. What does the box blot tell us about our class data?
2. Using the box plot, determine each of the following and describe what it tells us about our class:
1. The extremes (upper extreme and lower extreme)
2. The median
3. The lower quartile
4. The upper quartile
3. What are the benefits of using a box plot to represent class data?
4. What are the drawbacks of using a box plot to represent class data?

Differentiation

For the poster dot plot and box plot, consider having pre-made poster templates (with pre-drawn number lines).

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Provide sentence stems and/or anchor charts with definitions/examples of range, median, etc. for students who need support with sharing observations.

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For the GeoGebra box plot, consider sharing the data with students electronically via GeoGebra link so they don’t have to manually enter the data if data entry is an obstacle.

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For the assessment, consider asking students to fill in the blanks in one or more of the following statements:

• Approximately 25% (or ¼) of the data values fall between ___ and ___.
• Approximately 50% (or ½) of the data values fall between ___ and ___.
• Approximately 75% (or ¾) of the data values fall between ___ and ___.

Remediation

Extension/Enrichment

Ask students to use descriptive language to describe the shape and center of the data distribution.

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If outliers are present, ask students to collaborate on a definition for what qualifies as an outlier and predict what would happen to each statistic if the outlier was removed.

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Encourage students to move on and explore how to create box plots for two sets of data at the same time. Have them select their own data sets to work with.