SWBAT construct a viable argument by interpreting measures of center and spread in three different data sets.

Which basketball player would you value more: one who is very consistent or one who has a 1 in 3 chance of dropping over 40 points in a game?

5 minutes

For today's opener, we delve back into data that was collected on the stats survey a few weeks ago, by looking at the summary of answers submitted by students for the question:

**There is a lion running down the hall of North High School. It's coming right at you. What do you do?**

I let students arrive and take a look for themselves before asking, "who would like to interpret this graph?" Kids are always happy to volunteer. I record their "interpretations" on the board; here are examples from one class, and from another.

When I have four or so students statements on the board, I ask, "which of these statements are interpretations?" We go through the list one-by-one. In all of my classes, at least half of the lines I write are not really interpretations, but just observations about the data. I emphasize that it's not wrong to say that "58% of the students would run." Indeed, that's true. But it's just an observation about the data. "How might you interpret that statistic?" I ask.

We go through some possibilities. Usually students are willing to get the conversation started, but if they don't, I might say, "this data proves that 58% of the students are smart enough to not want to be eaten by a lion," or that "58% of the students are dumb enough to try to run away from a fast lion," or that "58% of the students are cowards." We assess the merit of each statement. "Which one of my interpretations is true?" I ask, and the truth is we don't know. By now, I hope that at least one student has equated interpretation with opinion, and that's something that I'll agree with when I hear it.

What I really want students to get is the point that different people might interpret the same data in different ways. The same data might be used for or against a given point. It's up to us to make connections between what the data says, and how we'd like to interpret it.

38 minutes

**The Task**

With the idea of interpretation in mind, I distribute the Evidence-Based Writing Prompt to which students will respond today.

Students are provided with the scenario that they are in charge of the New York Knicks and have to choose one of three star basketball players to sign to the team. They are given last season's scoring stats for each fictional player: scoring average, number of games played, and a plot of the number of points the player scored in each game. The twist is that the plot is different for each player. There is a histogram for one, a box plot for another, and a dot plot for the third.

The scoring averages are approximately the same for each player, but the median number of points in a game is different for each. There are also different measures of spread for each student. Also, two players played most of the season, and one played just 25 games. It's up to students to compare the data sets by noting these differences, and then to interpret these differences by using them to support a decision about which player they will sign. The task is designed so that a compelling argument could be made for any of the three players.

**Optional Scaffold: Writing Organizer**

Across subjects, students are learning the Claim-Explain-Evidence-Interpretation (CEEI) method at my school. As an optional scaffold, I've made this Outline & Organizer document. It helps for students to see a common structure across classes. I think that this one gets at what we need, but of course it's not the only format for organizing a piece of argumentative writing. The most important thing here - especially with the Common Core's emphasis on evidence-based argumentative writing - is that grade teams and schools choose some structure and share it, so that students can practice using the structure in different academic settings.

As a further scaffold, if necessary, I'll show students how to make a chart of players and statistical measures in the Evidence box.

**Work Time**

My ideal is to treat this as a summative assessment. I want kids to be able to show that they can find measures of center, spread and shape from a graph, compare those measures, and interpret them. In some classes, this is the case. In other classes, I'm ok with helping out a little if they need it. Many of my students have a hard time approximating the median and range from a histogram, so I'm ready to help with that if necessary.

If a student asks a straightforward question like "What are the measures of spread?" or "How do you find the mode?" I still treat this like a quiz, by telling them to consult their notes. If they ask me if their interpretation sounds good, I simply ask how it sounds to them.

This is a challenging assignment for many students, but it's not the last such assignment they'll have this year. As with everything we do, writing an argument based on data is a skill that takes practice, and that, through hard work, someone can get better at.