This activity gives students an opportunity to determine and request the information needed to create and use box plots to get information about distributions of data.

The Info Gap structure requires students to make sense of problems by determining what information is necessary, and then to ask for information that they need to solve the problems. This may take several rounds of discussion if their first requests do not yield the information they need (MP1). It also allows them to refine the language they use and to ask increasingly more precise questions until they get the information that they need (MP6).

After students have completed their work, share the correct answers and ask students to discuss the process of solving the problems. Here are some questions for discussion:

• “What information was helpful to ask for when determining which box plot might match the species of sea turtle?” (Anything from the five-number summary is helpful for narrowing down the choices of box plot.)
• “When you have a box plot, what is the easiest way to describe a typical value or variability?” (From a box plot, the median is the easiest measure of center to find, so that can be used for typical values. The IQR or range are both easy to find from a box plot to describe variability.)

Invite 2–3 students to share the norm they chose and how it supported the work of the group or a realization they had about a norm that would have worked better in this situation. Provide a sentence frame to help students organize their thoughts in a clear, precise way:

• “I picked the norm ‘.’ It really helped me/my group because .”

• “I picked the norm ‘​.’ During the activity, I realized that the norm ‘​’ would be a better focus because .”

The optional lesson provides students with a chance to practice finding a five-number summary from data, drawing a box plot, and then comparing distributions.

As students work, make sure that they correctly identify the five-number summary of each data set. If students have trouble making comparisons, prompt them to study the medians, IQRs, and ranges of the data sets. Then, notice how they compare the box plots and whether they interpret the different measures in the context of the given situation. If they make comparisons only in abstract terms (for example, “The median for both data sets are the same”), push them to specify what the comparisons mean in this situation (for example, “What does the equal median tell us in this context?”). Identify students who made sense of these numbers in terms of typical distances and consistency of the flights of each person's plane. Ask them to share later.

Focus the whole-class discussion on students’ analyses and interpretations of the box plots. Display the box plots for all to see.

Select a few students or groups to share their responses comparing Andre’s and Lin’s data. Be sure to discuss what it means when two data sets have the same median but different IQRs, as in Andre’s and Lin’s cases. If no students connect these values to the center and spread and data, ask them to do so. 

• “What can you say about the center of Andre’s data and that of Lin’s data?” (They have the same median of 28 yards.)
• “What does the same center tell us in this context?” (The same number could be used to describe a typical flight distance for both Andre’s and Lin’s flight distances.)
• “What can you say about the spread of Andre’s data and that of Lin’s data?” (Andre’s data are far more concentrated than Lin’s, which are quite spread out. The range of her data is 12 yards, which tells us there is much more variability in her flight distances. For Andre the range is only 5 yards, less than half of Lin’s, and his IQR is a quarter of Lin’s. Overall, there is much less variability in his data.)
• “Which of the two planes—Andre’s or Lin’s—flies a more consistent distance? How do you know?” (Andre’s, because the spread of his data is much smaller.)

Then, select a few other students or groups to compare Lin’s and Noah’s data. Be sure to discuss what it means when two data sets have the same spread (IQR in this case) but different medians.

• “What do the two very different centers tell us in this context?” (Generally speaking, a typical flight distance for Lin's plane is quite different from that for Noah’s.)
• “What can you say about the spreads of Lin’s and Noah’s data?” (Both sets have the same range and the same IQR, though the values of the quartiles are different for the two sets of data.)
• “What does the same range tell us in this case?” (The difference between the shortest flight distance and the longest one is the same for both data sets.)
• “What does the same IQR tell us in this case?” (The middle half of the two sets of data cover the same distance.)
• “Whose plane—Lin’s or Noah’s—flies a more consistent distance?” (Their planes fly with very similar consistency, or inconsistency. The identical IQR and range tell us that their data have very similar variability.)