SWBAT to generate a question that compares two groups relative to one characteristic, collect data, and summarize their findings. SWBAT compare the statistical center and spread of two different data sets.

Do girls always pay more for a haircut than boys? I wonder if boys send more texts than girls? Students generate a question they are interested in comparing two groups and use statistics to share their results.

30 minutes

The purpose of today's class is for students to work on a statistics project where they will generate their own question comparing two groups, collect data, and use what they have learned thus far to share their results. Before I explain the project to them, we start with a warm up question comparing some results about the costs of men's and women's haircuts. This problem can help them to see how they might design their own question and share their results. Unlike in previous problems, students are not working directly with the original data, but are starting with some of the key findings.

If I feel like I need to generate some enthusiasm about this work, I might start by asking how much, on average, a student pays for his/her haircut. Then I might lead the discussion to talk about the difference between men's and women's pricing and if it is fair. I always try to be careful when comparing gender in my class and might preface the discussion by saying that we are talking in broad terms for the purposes of this math work.

Next, we read through Haircut Costs together and students get to work sketching their box plots. They can work alone or in small groups. By now, students should be familiar with how to create a box plot. This is an important prerequisite. I want them to focus on comparing the two groups with regard to center, spread, and distribution, rather than on learning how to create the graph.

When students are finished with the sketches and the questions, I ask them to share out their findings. There is a lot to talk about here because the data are so different between the two groups. The main points I want students to touch on are:

- The differences in variability between the two groups. There is a much greater range of how much women pay for haircuts when compared to men. We can see this especially in the interquartile range.
- The skew of each data set to the right. We will spend some time talking about what this means as students often struggle to understand skew.
- The difference in the medians in both sets of data.
- The comparison of median to mean and why the median is a more accurate reflection of a "typical" cost for a haircut. The right skew will account for the higher mean in both data sets.

20 minutes

Next, I explain to students that they will be examining a question similar to the Hair Cut task for today's project:

I spend some time here helping students to generate a question that they can use to compare two groups at school (again, I'm sensitive here to potential stereotypes or inflammatory questions). I let students know that they will need to decide which two groups to compare with regard to one characteristic. Gender is an easy way for students to make comparisons but I might push them to think of other groups like underclassman and upperclassman or students who walk to school vs students who take the bus. Then we brainstorm possible differences.

I give students some time to generate their question and then we share out. I think this project works best for students to do individually or in pairs (at most). During the share out, some students may decide to change or tweak their question or groups they are comparing.

Next, I ask students to come up with a plan for collecting their data. Some students will write out a questionnaire, while others will conduct their survey verbally. We talk a little bit here about bias and how they can avoid bias in their data collection. I let them generate the ideas about how to do so and have them think about how they can set themselves up to get more reliable data.

Once each student has a question and a plan to collect data, we look at the Comparing 2 Sets of Data together. I may share deadlines with students or have them help me to determine when the project should be due. I leave time for questions about how they should present their findings.

10 minutes

I end today's class by having students complete Questions 1 and 2 on the Project Assignment. Students write down their question, including the two populations they want to compare and write about their method for collecting data.

I might also ask them to make a prediction about what they think they will find when they analyze their data. If so, I will have a few students share out their predictions at the close of class.

S-ID Haircut Costs is licensed by Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License

Source: http://www.illustrativemathematics.org/standards/hs