Box Plots

5 min

Narrative

The purpose of this Warm-up is to elicit the idea that it can be difficult to describe a distribution from the data alone, which will be useful when students visualize data using a box plot in a later activity. While students may notice and wonder many things about these data, the usefulness of data displays is the important discussion point.

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 table for all to see. Give students 1 minute of quiet time to look at the data set and to identify at least one thing they notice and at least one thing they wonder about the distribution of the data. Ask students to give a signal when they have noticed or wondered about something. When the minute is up, give students 1 minute to discuss their observations and questions with their partner. Follow with a whole-class discussion.

Student Task

Here are the birth weights, in ounces, of all the puppies born at a kennel in the past month.

What do you notice? What do you wonder?

  • 13
  • 14
  • 15
  • 15
  • 16
  • 16
  • 16
  • 16
  • 17
  • 17
  • 17
  • 17
  • 17
  • 17
  • 17
  • 18
  • 18
  • 18
  • 18
  • 18
  • 18
  • 18
  • 18
  • 19
  • 20

Sample Response

Students may notice:

  • The median birth weight is 17 ounces.
  • The median looks like it's the same as the mean.
  • Almost a third of the puppies weigh 18 ounces.
  • There are no gaps in the data or values that are very far from the center.
  • There are 25 puppies. 

Students may wonder:

  • If the IQR is less than 1.
  • How a histogram could be used to represent the data.
  • If a dot plot could be used to represent this data. 

Synthesis

Ask students to share the things that 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 data. 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 a visual display of the distribution does not come up during the conversation, ask students to discuss that idea.

Display the dot plot of the same data.

<p>A dot plot. Weight in ounces.</p>

Ask students:

  • “How would a data display like a dot plot help describe the distribution?” (It would be easier to see what is typical, estimate the center, and describe the spread.)
  • “Is it easier to find the mean from the data list or the dot plot? What about the median?” (It is easier to estimate the mean from the dot plot, but maybe a little easier to calculate it using the list. The median is probably a little easier to find from the list because this list is already organized.)
Standards
Addressing
  • 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