Using Dot Plots to Answer Statistical Questions
5 min
Teacher Prep
Setup
Narrative
In this lesson, students begin informally connecting center and spread to the word “typical.” They consider a value that could be typical or characteristic of a data set by thinking about two good options and reasonings. They continue to interpret a dot plot in the context of a situation (MP2). Students also have a chance to critique the arguments of Clare and Tyler (MP3).
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet work time and a minute to share their responses with a partner. Follow with a whole-class discussion.
During the partner discussion, identify students who agree with Clare or Tyler to share during the whole-class discussion.
Student Task
This dot plot shows the weights of backpacks, in kilograms, of 50 sixth-grade students at a school in New Zealand.
- The dot plot shows several dots at 0 kilograms. What could a value of 0 mean in this context?
-
Clare and Tyler studied the dot plot.
- Clare says, “I think we can use 3 kilograms to describe a typical backpack weight of the group because it has the greatest frequency.”
- Tyler disagrees and says, “I think 3 kilograms is too low to describe a typical weight. There are some values much greater than 3 and that should make the typical value greater.”
Do you agree with either of them? Explain your reasoning.
Sample Response
- Sample response: A value of 0 could represent students who don’t use backpacks.
- Sample response:
- I agree with Clare. There are more backpacks that are 3 kilograms than any other weights, and half of the dots are around 3 kilograms (between 2 and 4 kilograms).
- I agree with Tyler. Half of the values are 3 or less and half are 4 or more, but because the distribution goes all the way up to 16, it seems like that should move the typical value to greater than 3.
Activity Synthesis (Teacher Notes)
Ask the selected students—one who agrees with Clare and another who agrees with Tyler—to share their reasoning. Ask if anyone disagrees with both students, and if so, what value they would consider a better description of the center of the data.
Students should have a reasonable explanation for each argument they favor, but it is not necessary to confirm one way or another at this point.
Standards
- 6.SP.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- 6.SP.B.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- 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.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
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Using Dot Plots to Answer Statistical Questions
5 min
Teacher Prep
Setup
Narrative
In this lesson, students begin informally connecting center and spread to the word “typical.” They consider a value that could be typical or characteristic of a data set by thinking about two good options and reasonings. They continue to interpret a dot plot in the context of a situation (MP2). Students also have a chance to critique the arguments of Clare and Tyler (MP3).
Launch
Arrange students in groups of 2. Give students 2 minutes of quiet work time and a minute to share their responses with a partner. Follow with a whole-class discussion.
During the partner discussion, identify students who agree with Clare or Tyler to share during the whole-class discussion.
Student Task
This dot plot shows the weights of backpacks, in kilograms, of 50 sixth-grade students at a school in New Zealand.
- The dot plot shows several dots at 0 kilograms. What could a value of 0 mean in this context?
-
Clare and Tyler studied the dot plot.
- Clare says, “I think we can use 3 kilograms to describe a typical backpack weight of the group because it has the greatest frequency.”
- Tyler disagrees and says, “I think 3 kilograms is too low to describe a typical weight. There are some values much greater than 3 and that should make the typical value greater.”
Do you agree with either of them? Explain your reasoning.
Sample Response
- Sample response: A value of 0 could represent students who don’t use backpacks.
- Sample response:
- I agree with Clare. There are more backpacks that are 3 kilograms than any other weights, and half of the dots are around 3 kilograms (between 2 and 4 kilograms).
- I agree with Tyler. Half of the values are 3 or less and half are 4 or more, but because the distribution goes all the way up to 16, it seems like that should move the typical value to greater than 3.
Activity Synthesis (Teacher Notes)
Ask the selected students—one who agrees with Clare and another who agrees with Tyler—to share their reasoning. Ask if anyone disagrees with both students, and if so, what value they would consider a better description of the center of the data.
Students should have a reasonable explanation for each argument they favor, but it is not necessary to confirm one way or another at this point.
Standards
- 6.SP.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- 6.SP.B.4·Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
- 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.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.