# How can data be represented and summarized meaningfully?

• Revisit various ways to plot data: dot plots, histograms, and box plots (S-ID.A.1).

• Interpret plots of data within the context of the data (S-ID.A.3).

• Use the terms “symmetric” and “skewed” as descriptors of distributions (S-ID.A.2).

Students revisit the methods for representing and summarizing data that they learned in grades 6 to 8. They interpret dot plots, histograms, and box plots, attending to the referents of symbols used. Not just what are the quartile values, but what do they indicate about the data? Not just whether the graph is symmetric or skewed, but what does that tell us about the data?

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#### Description

WHAT: How is wealth distributed in America? Students interpret frequency graphs and calculate the mean and median income for citizens of three hypothetical countries. They recall that mean and median are measures of center, and while each tells you different information, neither gives you a complete picture of the data. We can better understand a set of data by analyzing how it is distributed. Then, they construct (S-ID.A.1) and compare box plots of the wealth distribution in the three countries. Students must use appropriate tools (by hand or using technology) strategically when creating the box plots (MP5). Finally, they confront the reality that the way wealth is distributed in the United States today is way more skewed than any of these.

WHY: Statistics are useful because they help us describe and compare data collected in our world. It is important to start this unit to use statistics in a meaningful way. Given the news in recent years about income inequality, and powerful entities rigging the system to skew wealth distribution even further, the utility of statistics for describing and modeling our reality is apparent (MP4).*Note that a paid subscription is required to access this resource.*

#### Description

WHAT: Each student gets a bag of M&M’s. They are asked to predict the distribution of colors, then to compare their predictions with the contents of their bags. They then compare results with those of their neighbors, combine totals, and compare these with those reported by the company that produces M&M’s. This requires collaboration, communication, and attention to precision (MP6). Students represent their data graphically in at least one way and are challenged to represent it in multiple ways (S-ID.A.1).

WHY: This activity does not have heavy algebraic demands so it gives all students an entry point into discussion of data collection, sample size, and data representation.