The mathematical purpose of this activity is for students to write a statistical question for dropping and catching a ruler under different conditions.

The goal of this discussion is to make sure that everyone has a statistical question about reaction time that will require collecting data from two different conditions to test.

Check student questions and assist them in creating a question that meets the requirement. Here are some questions for discussion.

• “What are your two conditions?” (Standing on one foot and standing on both feet.)
• “How are you going to collect these data values?” (I will hold and drop the ruler while my partner stands on one foot. Then I will repeat this while my partner is standing on two feet.)
• “How many trials do you think you should do under each condition?” (At least ten)

The mathematical purpose of this activity is for students to design an experiment to answer a statistical question, to collect data, to analyze data using statistics, and to communicate the answer to the statistical question using a display. It may be helpful to have multiple groups combine to allow students to experience the different conditions for many experiments. Making statistical technology available gives students an opportunity to choose appropriate tools strategically (MP5).

Notice groups that create displays that communicate their mathematical thinking clearly, contain an error that would be instructive to discuss, or organize the information in a way that is useful for all to see.

Select groups to share their visual displays. Encourage students to ask questions about the mathematical thinking or design approach that went into creating the display. For students who had an error in their display, ask “What error do you see in the display and how would you resolve it?” (Sample responses:

• I noticed that they used the mean instead of the median. I would resolve it by using the median since there was an outlier
• I noticed that the IQR was calculated incorrectly. I would have used technology to verify my statistics.)

Here are questions for discussion, if not already mentioned by students:

• “Once you collected your data, how did you answer your statistical question?” (I used two different dot plots to display my data and determined that the mean was the most appropriate measure of center because my dot plots were approximately symmetric. I then calculated the standard deviation using technology because standard deviation is appropriate to use with the mean. I then compared the mean and the standard deviation for the two sets of data and determined that standing on two feet gave my partner a slightly faster reaction time and showed less variability than standing on one foot did.)
• “How did you choose which measure of center and which measure of variability to use?” (I used the distribution shape to determine the measure of center. My data distribution was skewed, so I used the median. I used the IQR as a measure of variability because it is based on the median. If I had used the mean, I would have used the standard deviation.)
• “Using the context of the two treatments, what did the measure of variability tell you?” (The measure of variability told me how spread apart the results were from the measure of center I chose. It let me know how consistent the reaction time was for each treatment.)
• “Imagine that you collected data for the same treatments from all the students in the class. How would this change how you displayed or analyzed your data?” (There would be a lot of data. I would probably have to use technology to find the statistics and to create the data display. I think that I might need to use a histogram to represent the distribution of the data.)

In this activity, students use a large data set to compare the size of students with different dominant hands. Students must choose the appropriate tools (MP5) to analyze a large data set such as this. Additional variables are provided if students wish to extend their analysis to find any other connections, although bivariate data are the focus of a future unit in this course.

Select students to share their analysis of the data.