Interpreting Histograms
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to connect the analytical work that students have done with dot plots in previous lessons with statistical questions. This activity reminds students that we gather, display, and analyze data in order to answer statistical questions. This work will be helpful as students contrast dot plots and histograms in subsequent activities.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time, followed by 2 minutes to share their responses with a partner. Ask students to decide, during a partner discussion, if each question proposed by their partner is a statistical question that can be answered using the dot plot. Follow with a whole-class discussion.
If students have trouble getting started, consider giving a sample question that can be answered using the data on the dot plot (for example, “How many dogs weigh more than 100 pounds?”)
Student Task
Here is a dot plot showing the weights, in pounds, of 40 dogs at a dog show.
- Write two statistical questions that can be answered using the dot plot.
- What would you consider a typical weight for a dog at this dog show? Explain your reasoning.
Sample Response
- Sample questions:
- How many dogs weigh exactly 70 pounds?
- How many dogs weigh more than 80 pounds but less than 150 pounds?
- How much does the heaviest dog at the dog show weigh?
- How many times as heavy as the lightest dog is the heaviest dog?
- How alike or different are the weights of the dogs at the show?
- Sample responses:
- About 114 pounds, because the largest percentage of the dots are at 114, and it seems to be about where the center of the data is.
- About 100 pounds, because about half of the dogs are 100 pounds or lighter, and half are heavier than 100 pounds.
Activity Synthesis (Teacher Notes)
Ask students to share questions that they agreed were statistical questions that could be answered using the dot plot. If there is time, consider asking students how they would find the answer to some of the statistical questions.
Display the dot plot for all to see. Ask students to share a typical weight for a dog at this dog show and why they think it is typical. Mark their answers on the displayed dot plot. After each student shares, ask the class if they agree or disagree.
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.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
- 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.A.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
10 min
20 min
Knowledge Components
All skills for this lesson
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Interpreting Histograms
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to connect the analytical work that students have done with dot plots in previous lessons with statistical questions. This activity reminds students that we gather, display, and analyze data in order to answer statistical questions. This work will be helpful as students contrast dot plots and histograms in subsequent activities.
Launch
Arrange students in groups of 2. Give students 1 minute of quiet work time, followed by 2 minutes to share their responses with a partner. Ask students to decide, during a partner discussion, if each question proposed by their partner is a statistical question that can be answered using the dot plot. Follow with a whole-class discussion.
If students have trouble getting started, consider giving a sample question that can be answered using the data on the dot plot (for example, “How many dogs weigh more than 100 pounds?”)
Student Task
Here is a dot plot showing the weights, in pounds, of 40 dogs at a dog show.
- Write two statistical questions that can be answered using the dot plot.
- What would you consider a typical weight for a dog at this dog show? Explain your reasoning.
Sample Response
- Sample questions:
- How many dogs weigh exactly 70 pounds?
- How many dogs weigh more than 80 pounds but less than 150 pounds?
- How much does the heaviest dog at the dog show weigh?
- How many times as heavy as the lightest dog is the heaviest dog?
- How alike or different are the weights of the dogs at the show?
- Sample responses:
- About 114 pounds, because the largest percentage of the dots are at 114, and it seems to be about where the center of the data is.
- About 100 pounds, because about half of the dogs are 100 pounds or lighter, and half are heavier than 100 pounds.
Activity Synthesis (Teacher Notes)
Ask students to share questions that they agreed were statistical questions that could be answered using the dot plot. If there is time, consider asking students how they would find the answer to some of the statistical questions.
Display the dot plot for all to see. Ask students to share a typical weight for a dog at this dog show and why they think it is typical. Mark their answers on the displayed dot plot. After each student shares, ask the class if they agree or disagree.
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.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
- 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.A.3·Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.