Using Box Plots
10 min
Teacher Prep
Setup
Narrative
This Warm-up allows students to practice creating a box plot from a five-number summary and to think about the types of questions that can be answered using the box plot. To develop questions based on the box plot prompts students to put the numbers of the five-number summary into context (MP2).
As students work, identify a student who has clearly and correctly drawn the box plot. Ask that student to share during the whole-class discussion.
For the second question, some students may write decontextualized questions that are simply about parts of the box plot like “What is the IQR?” or “What is the range?” Others might write contextualized questions that the box plot could help to answer like “What is the least amount of sleep in this data set?” or “What is the median number of hours of sleep for this group?” Identify a few students from each group so that they can share later.
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet work time, followed by a whole-class discussion.
Select students with types of questions, such as those suggested in the activity narrative, to share later.
Student Task
Ten sixth-grade students are asked how much sleep, in hours, they usually get on a school night. Here is the five-number summary of their responses.
- Minimum: 5 hours
- First quartile: 7 hours
- Median: 7.5 hours
- Third quartile: 8 hours
- Maximum: 9 hours
-
On the grid, draw a box plot for this five-number summary.
- What questions could be answered by looking at this box plot?
Sample Response
-
- Sample responses:
- What is the least amount of sleep a student usually gets on a school night?
- How many students usually get at least 7 hours of sleep on a school night?
Activity Synthesis (Teacher Notes)
Select the previously identified student with a correct box plot to display it for all to see. If that is not possible, ask the student to share how they drew the box plot, and record and display the drawing based on the student’s directions.
Select other previously identified students to share questions that could be answered by looking at the box plot. First, ask the questions that can be answered without the context, and then ask the questions that rely on the context. Record and display these questions for all to see. After each question, ask the rest of the class if they agree or disagree that the answer can be found using the box plot. If time permits, ask students for the answer to each shared question.
Point out questions that are contextualized versus those that are not. Explain that a box plot can help us to make sense of a data set in context and can help answer questions about a group or a characteristic of a group in which we are interested. The different measures that we learned to identify or calculate help to make sense of a data distribution in context.
Standards
- 6.SP.1·Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. <em>For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.</em>
- 6.SP.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- 6.SP.A.1·Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. <span>For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students' ages.</span>
- 6.SP.B.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Using Box Plots
10 min
Teacher Prep
Setup
Narrative
This Warm-up allows students to practice creating a box plot from a five-number summary and to think about the types of questions that can be answered using the box plot. To develop questions based on the box plot prompts students to put the numbers of the five-number summary into context (MP2).
As students work, identify a student who has clearly and correctly drawn the box plot. Ask that student to share during the whole-class discussion.
For the second question, some students may write decontextualized questions that are simply about parts of the box plot like “What is the IQR?” or “What is the range?” Others might write contextualized questions that the box plot could help to answer like “What is the least amount of sleep in this data set?” or “What is the median number of hours of sleep for this group?” Identify a few students from each group so that they can share later.
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet work time, followed by a whole-class discussion.
Select students with types of questions, such as those suggested in the activity narrative, to share later.
Student Task
Ten sixth-grade students are asked how much sleep, in hours, they usually get on a school night. Here is the five-number summary of their responses.
- Minimum: 5 hours
- First quartile: 7 hours
- Median: 7.5 hours
- Third quartile: 8 hours
- Maximum: 9 hours
-
On the grid, draw a box plot for this five-number summary.
- What questions could be answered by looking at this box plot?
Sample Response
-
- Sample responses:
- What is the least amount of sleep a student usually gets on a school night?
- How many students usually get at least 7 hours of sleep on a school night?
Activity Synthesis (Teacher Notes)
Select the previously identified student with a correct box plot to display it for all to see. If that is not possible, ask the student to share how they drew the box plot, and record and display the drawing based on the student’s directions.
Select other previously identified students to share questions that could be answered by looking at the box plot. First, ask the questions that can be answered without the context, and then ask the questions that rely on the context. Record and display these questions for all to see. After each question, ask the rest of the class if they agree or disagree that the answer can be found using the box plot. If time permits, ask students for the answer to each shared question.
Point out questions that are contextualized versus those that are not. Explain that a box plot can help us to make sense of a data set in context and can help answer questions about a group or a characteristic of a group in which we are interested. The different measures that we learned to identify or calculate help to make sense of a data distribution in context.
Standards
- 6.SP.1·Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. <em>For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.</em>
- 6.SP.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- 6.SP.A.1·Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. <span>For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students' ages.</span>
- 6.SP.B.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.