This unit is a brief overview of some key statistical concepts. First, 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.

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.  

The unit concludes with an optional section exploring probability. Students are introduced to probability as a way to quantify how likely an event is to happen. They explore the connection between probability and results of repeated experiments, ways to examine the sample space for more complex experiments, and simulating experiments. 

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.

Progression of Disciplinary Language

In this unit, teachers can anticipate students using language for mathematical purposes, such as comparing, interpreting, and justifying. 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:

Compare

• Questions that produce numerical and categorical data (Lesson 1).
• Dot plots and histograms (Lesson 3).
• Features and distributions of data sets (Lessons 4 and 5).
• Measures of center with samples (Lesson 9).
• Sampling methods (Lesson 10).
• Methods for writing sample spaces (Lesson 15).

Interpret

• Dot plots (Lessons 2 and 5).
• Histograms (Lesson 3).
• Mean of a data set (Lesson 4).
• Five-number summaries and box plots (Lesson 7).
• Situations involving populations and samples (Lesson 8).
• Situations involving sample spaces and probability (Lesson 16).

Justify

• Reasoning for matching data sets to questions (Lesson 1).
• Reasoning about mean and median (Lesson 6).
• Which samples are or are not representative of a larger population (Lesson 9).
• Which samples correspond with different populations (Lesson 11).
• Whether situations are surprising and possible (Lesson 14).

In addition, students are expected to represent data using dot plots, histograms, five-number summaries, and box plots, and to represent probabilities using sample spaces. Students also have opportunities to use language to describe features of a data set, describe patterns observed in repeated experiments, and explain how to use a simulation to answer questions about the situation.

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.