In this unit, students learn about populations and study variables associated with a population. They begin by classifying questions as either statistical or non-statistical—based on whether variable data is necessary to answer the question. This leads to further investigation into variability and data displays, such as dot plots and histograms. As students visualize data, they begin to describe the distribution of data more precisely as they work with mean and mean absolute deviation (MAD).

After working with those statistics, students begin to recognize that some distributions are not well-suited to description by mean and MAD. Students are introduced to median, range, and interquartile range as additional measures of center and variability that can be used to describe distributions in some situations. That also leads to the box plot as an additional way to visualize data.

Note that the introduction of mean absolute deviation is used as an introductory model for understanding variability. Although standard deviation is more mathematically useful, its calculation and meaning may be difficult for students at this level without an understanding of normal distributions. In later courses, when student understanding of variability and their exposure to additional distributions is expanded, students will learn about standard deviation and evolve their understanding away from mean absolute deviation.

Box plots and dot plots for two sets of data: "pug weights in kilograms” and "beagle weights in kilograms". The numbers 6 through 11 are indicated and there are tick marks midway between each indicated number. Each box plot is above it's corresponding dot plot. The approximate data for the box plot for "pug weights in kilograms" are as follows: Minimum value, 6. Maximum value, 8. Q1, 6.5. Q2, 7. Q3, 7.3. The approximate data for the dot plot for "pug weights in kilograms" are as follows: 6 kilograms, 1 dot. 6.2 kilograms, 2 dots. 6.4 kilograms, 2 dots. 6.6 kilograms, 2 dots. 6.8 kilograms, 2 dots. 7 kilograms, 3 dots. 7.2 kilograms, 3 dots. 7.4 kilograms, 1 dot. 7.6 kilograms, 2 dots. 7.8 kilograms, 1 dot. 8 kilograms, 1 dot. The approximate data for the box plot for "beagle weights in kilograms" are as follows: Minimum value, 9. Maximum value, 11. Q1, 9.6. Q2, 10. Q3, 10.5. The approximate data for the dot plot for "beagle weights in kilograms" are as follows: 9 kilograms, 1 x. 9.2 kilograms, 2 x's. 9.4 kilograms, 1 x. 9.6 kilograms, 3 x's. 9.8 kilograms, 1 x. 10 kilograms, 3 x's. 10.2 kilograms, 3 x's. 10.4 kilograms, 1 x. 10.6 kilograms, 2 x's. 10.8 kilograms, 2 x's. 11 kilograms, 1 x.  

Progression of Disciplinary Language

In this unit, teachers can anticipate students using language for mathematical purposes, such as justifying, representing, and interpreting. Throughout the unit, students will benefit from routines designed to grow robust disciplinary language, both for their own sense-making and for building shared understanding with peers. Teachers can formatively assess how students are using language in these ways, particularly when students are using language to:

Justify

• Reasoning for matching data sets to questions (Lesson 2).
• Reasoning about dot plots (Lesson 3).
• Reasoning about mean and median (Lesson 13).
• Reasoning about changes in mean and median (Lesson 14).
• Reasoning about which information is needed (Lesson 17).
• Which summaries and graphs best represent given data sets (Lesson 18).

Represent

• Data using dot plots (Lessons 3 and 4).
• Data using histograms (Lesson 7).
• Mean using bar graphs (Lesson 9).
• Data with five number summaries (Lesson 15).
• Data using box plots (Lesson 16).

Interpret

• Dot plots (Lessons 4 and 11).
• Histograms (Lessons 6 and 18).
• Mean of a data set (Lesson 9).
• Five-number summaries (Lesson 15).
• Box plots (Lesson 16).

In addition, students are expected to critique the reasoning of others, describe how quantities are measured, describe and compare features and distributions of data sets, generalize about means and distances in data sets, generalize categories for sorting data sets, and generalize about statistical questions. Students are also expected to use language to compare questions that produce numerical and categorical data, compare dot plots and histograms, and compare histograms and bar graphs.

The table shows lessons where new terminology is first introduced in this course, including when students are expected to understand the word or phrase receptively and when students are expected to produce the word or phrase in their own speaking or writing. Terms that appear bolded are in the Glossary. Teachers should continue to support students’ use of a new term in the lessons that follow where it was first introduced.