## Task

In Mrs. Sanchez' math classroom, more people sit on the right-hand side of the room than the left. The students on the right-hand side of the classroom received the following scores on an exam worth 100 points:

$$ 85,\, 90,\, 100,\, 95,\, 0,\, 0,\, 90,\, 70,\, 100,\, 95,\, 80,\, 95 $$

The students on the left received these test scores:

$$65,\, 80,\, 90,\, 65,\, 80,\, 60,\, 95,\, 85$$

- Make two box plots of the students' scores, one for each side of the room.
- Make a statistical argument that the students on the right-hand side were more successful.
- Make a statistical argument that the students on the left-hand side were more successful.

## IM Commentary

The goal of this task is to critically compare the center and spread of two data sets. Although the mean is not specifically requested, it can be used as an argument in favor of the left's performance. The teacher may wish to request or suggest for students to calculate the mean or tell them that the statistical arguments for (b) and (c) should not just be based on the box plots. The teacher will also want to make sure that the two box plots can be directly compared so the values on the two number lines of the boxplots need to correspond to one another.

Statistics is a powerful tool for supporting arguments in a variety of contexts: medicine, education, sports, and ecology to name a few. There are usually choices to make, however, both in which statistics to use and how they are reported. This task gives students an opportunity to think carefully about how to analyze the data in order to support a particular point of view.

This task is based on an idea used for a worksheet developed for one of the UCLA Curtis Center's Saturday trainings given on December 6, 2014. In that problem, two students' quiz scores were compared and the structure of the numbers were very similar.