Using Histograms to Answer Statistical Questions

5 min

Teacher Prep
Setup
Students in groups of 2–4. A minute of quiet think time, 2 minutes of small-group discussion, followed by a whole-class discussion.

Narrative

In this Warm-up, students use the terminology they have learned in the unit so far to describe questions. Students are reminded to talk about statistical questions, numerical and categorical data, and typical values. Students have the chance to practice being precise in their mathematical language (MP6).

Launch

Arrange students in groups of 2–4. Display mathematical vocabulary related to questioning and data already discussed in the unit such as:

  • Numerical data.
  • Categorical data.
  • Statistical question.
  • Typical value.
  • Spread.
  • Variability.

Student Task

Here are four questions about the population of Alaska. 

Describe the questions as precisely as you can.

  1. In general, at what age do Alaska residents retire?
  2. At what age can Alaskans vote?
  3. What is the age difference between the youngest and oldest Alaska residents with a full-time job?
  4. Which age group is the largest part of the population: 18 years or younger, 19–25 years, 25–34 years, 35–44 years, 45–54 years, 55–64 years, or 65 years or older?

Sample Response

Sample responses:

  1. A statistical question that requires numerical data. The answer will be the typical value.
  2. A non-statistical question that will have a numerical answer.
  3. A statistical question that requires numerical data. The answer is based on how spread out the data are.
  4. A statistical question that requires categorical data. The category with the most data is the answer.
Activity Synthesis (Teacher Notes)

For each question, invite a group to share how they described the question. After the group shares, invite other groups to add any additional information. If necessary, direct students to the displayed list of words to help students use more formal language.

Standards
Addressing
  • 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.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·Summarize and describe distributions.
  • 6.SP.B·Summarize and describe distributions.

20 min

10 min