Students look at different examples of distribution shapes and their descriptions and decide whether or not they are correct descriptions of the given distribution shapes. Whether the students agree or disagree with the descriptions, they will explain why. When students explain their answers, it allows others to focus on critiquing the explanations given (MP3). This prepares students for a later lesson when they have to decide which data displays depict the same data set. To be successful with that task, students will have to remember the importance of distribution shapes. This activity also prepares students to create statistical questions or situations based solely on a distribution shape, because they will understand what the shape means about the data set and what types of data sets make sense for a given distribution shape.

If students think that "symmetric" is equivalent to "bell-shaped," consider asking:

• "Explain what ‘symmetric’ and ‘bell-shaped’ mean."

• "If a distribution is bell-shaped, does it have to be symmetric? If a distribution is symmetric, does it have to be bell-shaped?"

The goal of this activity is for students to be able to explain why a distribution shape is labeled as its respective shape. Review correct answers as a whole group, if time permits.

In this activity, students practice using mathematical language to describe the shape of distributions. Students attend to the precision of their language (MP6), including using the term “approximately” as needed.

The goal of this activity is for students to recognize visual differences in distribution shapes. To help achieve this, highlight word meanings to help students remember some differences. Discuss some meanings (math-related or not) of each vocabulary word and how the word relates to the distribution shape. Here are sample questions and sentence starters to promote a class discussion:

• “In geometry, what does ‘symmetric’ mean? How does that relate to the data distributions that we labeled as such?” (“Symmetric” means parts of a figure match up after a transformation. Here, we specifically mean there is a line of reflection over which the left and right half match up. The data distributions that can be folded on a vertical line with the two sides matching up are called “symmetric.” It is important to note that distributions can be described as symmetric even if they do not have perfect symmetry. For example, the uniform histogram is also symmetric, even though a few intervals are at slightly different heights than their counterparts on the other side.)
• “‘Uniform’ means the same, so data distributions are uniform when ________.” (the dots in dot plots are all stacked to about the same height; histogram intervals are all about the same height)
• “What does it mean for a data distribution to be bell-shaped?” (It means the data distribution is shaped like a “bell”—higher in the middle, and lower at each end.)
• “‘Skewed,’ in mathematics, means not symmetric, so skewed data distributions have data points that _________.” (are more frequent on one side of the distribution than the other side)
• “How do you know when a data distribution is skewed? What does this usually mean about the data set?” (You know it is skewed when the shape of the data is not symmetric, so there are more values on one side of the typical values than on the other.)
• “If a distribution shape is uniform, what can you say about all its data points?” (They are exactly the same or similar in frequency.)
• “Is the shape of a data distribution enough to fully explain a data set? If not, what other characteristics can we use to describe data?” (No, since it does not say what the actual values are. Measures of center and variability, the five-number summary, and the frequency of values in certain intervals can also be useful in describing the data.)