Using Data to Solve Problems

5 min

Teacher Prep
Setup
Students in groups of 2. 2 minutes of quiet work time for the first question, 2 minutes of partner collaboration on the second question.

Narrative

This Warm-up allows students to review two important ideas of this unit: interpreting data in a box plot and writing statistical questions based on a data set. Students write statistical questions based on given box plots, and then they trade questions to answer questions written by another student.

Launch

Arrange students in groups of 2. Tell students that, for the first question, one partner should write two questions about the head lengths and the other partner should write two questions about the head widths.  For the second question, they should exchange and review each other's questions. If their partner's question does not seem to be a statistical question, suggest a revision so that it becomes a statistical question, and then answer the question. Remind students to consider units of measurement.

Give students 2 minutes of quiet work time for the first question and 2 minutes for collaboration afterward. 

Student Task

In one study on wild bears, researchers measured the head lengths and head widths, in inches, of 143 wild bears. The box plots summarize the data from the study.

A set of two box plots, head length in inches, from 2 to 20 by ones.
A set of two box plots, head length in inches, from 2 to 20 by ones. Top box plot labeled male bears. Whisker from 9 to 12 point 5. Box from 12 point 5 to 15 point 5 with vertical line at 13 point 5. Whisker from 15 point 5 to 18 point 5. Bottom box plot labeled female bears. Whisker from 10 to 12. Box from 12 to 13 point 5 with vertical line at 12 point 5. Whisker from 13 point 5 to 15 point 5.

A set of two box plots, head width in inches, from 2 to 20 by ones.
A set of two box plots, head width in inches, from 2 to 20 by ones. Top box plot labeled male bears. Whisker from 4 to 5 point 5. Box from 5 point 5 to 8 with vertical line 6 point 5. Whisker from 8 to 10. Bottom box plot whisker from 4 point 5 to 5. Box from 5 to 6 point 5 with vertical line at 6. Whisker from 6 point 5 to 7 point 5.

  1. Write four statistical questions that could be answered using the box plots: two questions about the head length and two questions about the head width.

  2. Trade questions with your partner.

    1. Decide if each question is a statistical question.
    2. Use the box plots to answer each question.

Sample Response

Sample responses:

    • What is a typical head length, in inches, for male bears in the data set?
    • Do female bears generally have longer heads than male bears?
    • Which data set shows more variability in head widths: male bears or female bears?
    • What is the widest head width, in inches, for male bears?
    • How do the ranges of head widths compare? Which group—male bears or female bears—has a larger range, and by how much?

    • A typical head length for male bears is about 13.5 inches.

    • No, female bears generally have shorter heads than male bears.

    • The data for male bears show more variability in head width.

    • The widest head width for male bears is 10 inches.

    • Male bears have a larger range of head widths. It is nearly twice as large as female bears' range of head widths. The range for male bears is about 6 inches, and the range for female bears is a little over 3 inches.

Activity Synthesis (Teacher Notes)

Ask several students to share their questions about the head width and head length. Record and display their responses for all to see. After each student shares, ask the class if they agree or disagree that it is a statistical question. If they agree, ask how they would find the answer, or ask for the answer itself. If they disagree, ask how they could rewrite the question so that it is a statistical question. 

Standards
Addressing
  • 6.SP.2·Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
  • 6.SP.A.2·Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.