Quartiles and Interquartile Range
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to elicit the idea that there are multiple ways to describe variability, which will be useful when students learn about range and interquartile range in a later activity. While students may notice and wonder many things about these dot plots, variability and how to measure it are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language that they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly
Launch
Arrange students in groups of 2. Display the dot plots for all to see. Ask students to think of at least one thing that they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things that they notice and wonder about.
Student Task
Here are dot plots that show the ages of people at two different parties. The mean of each distribution is marked with a triangle.
What do you notice and what do you wonder about the distributions in the two dot plots?
Sample Response
Students may notice:
- The mean of the two data sets are different. The mean for the second data set is 5 years higher than that for the first.
- The range in values of the two data sets are about the same.
- Most points in the first data set are clustered around 8 and 10 with only a few that are much higher.
- The mean for the first data set is located where there are no points.
- The points in the second data set are not clustered anywhere. They are distributed along the dot plot, between 5 and 42 years.
- The MAD values are close for the two data sets.
Students may wonder:
- Why the data distributions look so different.
- How the MAD values are the same or close.
- If there could be other distributions that look very different from these two but also have the same MAD.
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses for all to see, without editing or commentary. If possible, record the relevant reasoning on or near the dot plots. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.
If the idea that the MAD does not describe the variability of these two sets well does not come up during the conversation, ask students to discuss that idea.
Two key ideas to uncover here are:
- The MAD is a way to summarize variation from the mean, but the single number does not always tell us how the data are distributed.
- The same MAD could result from very different distributions.
Standards
- 6.SP.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- 6.SP.5.d·Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- 6.SP.B.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- 6.SP.B.5.d·Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
15 min
15 min
Knowledge Components
All skills for this lesson
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Quartiles and Interquartile Range
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to elicit the idea that there are multiple ways to describe variability, which will be useful when students learn about range and interquartile range in a later activity. While students may notice and wonder many things about these dot plots, variability and how to measure it are the important discussion points.
When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language that they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly
Launch
Arrange students in groups of 2. Display the dot plots for all to see. Ask students to think of at least one thing that they notice and at least one thing they wonder. Give students 1 minute of quiet think time, and then 1 minute to discuss with their partner the things that they notice and wonder about.
Student Task
Here are dot plots that show the ages of people at two different parties. The mean of each distribution is marked with a triangle.
What do you notice and what do you wonder about the distributions in the two dot plots?
Sample Response
Students may notice:
- The mean of the two data sets are different. The mean for the second data set is 5 years higher than that for the first.
- The range in values of the two data sets are about the same.
- Most points in the first data set are clustered around 8 and 10 with only a few that are much higher.
- The mean for the first data set is located where there are no points.
- The points in the second data set are not clustered anywhere. They are distributed along the dot plot, between 5 and 42 years.
- The MAD values are close for the two data sets.
Students may wonder:
- Why the data distributions look so different.
- How the MAD values are the same or close.
- If there could be other distributions that look very different from these two but also have the same MAD.
Activity Synthesis (Teacher Notes)
Ask students to share the things they noticed and wondered. Record and display their responses for all to see, without editing or commentary. If possible, record the relevant reasoning on or near the dot plots. Next, ask students, “Is there anything on this list that you are wondering about now?” Encourage students to respectfully disagree, ask for clarification, or point out contradicting information.
If the idea that the MAD does not describe the variability of these two sets well does not come up during the conversation, ask students to discuss that idea.
Two key ideas to uncover here are:
- The MAD is a way to summarize variation from the mean, but the single number does not always tell us how the data are distributed.
- The same MAD could result from very different distributions.
Standards
- 6.SP.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- 6.SP.5.d·Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
- 6.SP.B.5.c·Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.
- 6.SP.B.5.d·Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.