Box plot match
Match the cumulative frequency curves with their corresponding box plots.
Problem
Box Plot Match printable sheet
Here are six cumulative frequency graphs and six box plots of the same data.
Can you match them up?
With thanks to Don Steward, whose ideas formed the basis of this problem.
Student Solutions
Teachers' Resources
Possible approach
Distribute the graphs and box plots to students in pairs or small groups, either as a worksheet or cut up into cards for matching. Explain that there are six datasets, and for each one, a cumulative frequency curve and a box plot has been drawn. The challenge is to match each cumulative frequency curve to the box plot that represents the same data.
Explain that for any pair of cards they match, students must convince the other members of their group. By the end, they should be able to justify each of their pairings.
As you circulate, listen for which pairings students tend to find easiest, and for any common misconceptions. If any pairs/groups are slow to progress, you could let them know which cards other groups matched first. If some cards are matched incorrectly, allow students to finish before pointing this out - once they have cards left at the end that do not match, they will have to run through their reasoning again and search for their mistakes. Also listen out for students starting to make more general statements about features of the graphs and of the box plots they match with.
Once all groups have made good progress, discuss their reasoning as a whole group. Begin with pairings they agree on - can they build on each others' justifications to explain why they match? If there are any they disagree on, then this is a great opportunity to compare arguments and collaborate to find the true match, and the best explanation.
Possible support
Before introducing the game, you could present students with some data (maybe two different small datasets) and ask them to sketch a cumulative frequency curve and box plot for the data. They could briefly compare the properties of the box plot with those of the cumulative frequency curve, and explain those based on the underlying data.
Possible extension
Students could come up with some of their own cumulative frequency curves and matching box plots, including making up underlying data if it helps. Challenge them to create a set of cards that can be unambiguously matched, and/or a set of cards where it is not possible to tell which box plots match which cumulative frequency curves.