The goal of this activity is for students to be introduced to the idea that variability is important when analyzing and comparing data sets. Students will compare data sets, and make a decision as to which data set represents a better situation. This activity prepares students to calculate variability to compare data sets in a later lesson. Monitor for students who calculate any statistics to inform their decisions. Make note of the students who calculate only a measure of center vs. students who calculate both a measure of center and a measure of variability.

Making statistical technology available gives students an opportunity to choose appropriate tools strategically (MP5).

Use Stronger and Clearer Each Time to give students an opportunity to revise and refine their response to which gas station they would choose. In this structured pairing strategy, students bring their first draft response into conversations with 2–3 different partners. They take turns being the speaker and the listener. As the speaker, students share their initial ideas and read their first draft. As the listener, students ask questions and give feedback that will help clarify and strengthen their partner’s ideas and writing.

If time allows, display these prompts for feedback:

• “ makes sense, but what do you mean when you say ?”

• “Can you describe that another way?”

• “Which is more important: the chance of a low price or consistency?”

Close the partner conversations, and give students 2–3 minutes to revise their first draft. Encourage students to incorporate any good ideas and words they got from their partners to make their next draft stronger and clearer. If time allows, invite students to compare their first and final drafts. Select 2–3 students to share how their drafts changed and why they made the changes they did.

The purpose of this discussion is to understand that the variability is worth paying attention to. If any students chose to compute the mean, median, IQR, MAD, or range for the two stations, ask them to share their results and how those values help them decide. Interestingly, the mean is the same for the gas stations. But any measure of variability shows that the prices at Station B are more stable and predictable than the prices at Station A. If no students suggest computing measures of center and variability and comparing them, be prepared to demonstrate.

Here are the summary statistics for each set of data:

• For Station A:

  • Mean: 2.94
  • Five-number summary: 2.38, 2.68, 2.86, 3.26, 3.59
  • Range: 1.21
  • IQR: 0.58
  • MAD: 0.29

• For Station B:

  • Mean: 2.94
  • Five-number summary: 2.84, 2.85, 2.95, 3.03, 3.05
  • Range: 0.21
  • IQR: 0.18
  • MAD: 0.07

If time permits, discuss which measures are helpful. Here are sample questions:

• “Was the mean helpful in deciding the gas station from which you would buy gas?” (No, because both means were the same.)
• “How did the range (or IQR, MAD, five-number summary) help you decide which gas station you would go to?” (Whichever gas station had the highest range [or IQR or MAD] is the gas station I chose.)
• “In the real world, how would you use the gas prices at each gas station to make a decision?” (I would think about which one generally had lower prices and choose that one, or I would see which one had more predictably cheaper prices and choose that one.)

The purpose of this activity is for students to practice using measures of center and measures of variability to compare data sets. Students look at each pair of data sets and choose the better situation on the basis of the variability of each. In comparing the data sets, students apply statistics to real-world situations. This activity prepares students to make comparisons of data in a later lesson in which they must order data sets from least variable to most variable. Students should record their answers for each comparison, and they will be used in a later extra-support lesson. In this activity, students construct viable arguments (MP3) when they explain their reasoning behind a choice of situations using statistics from data given.

The goal of this activity is for students to know that measures of variability are very useful when analyzing and comparing data and ultimately making decisions in the real world. Here are sample questions to promote class discussion:

• “How might the median help you make decisions about situations like these?” (If there is a big difference between the medians, I might choose the one with a more favorable value.)
• “How might the interquartile range help you make decisions about situations like these?” (If the medians are about the same, the IQR could help in deciding which options are more consistent and which are more variable.)
• “What are some other situations for which you might use statistics like these to compare two options in your life?” (I could think about statistics to help make decisions between the best garden materials to help grow plants or reduce weeds, and to choose between things on the basis of their ratings from other people.)