# Statistics

Students investigate how to use sampling to make inferences about larger populations of interest, engaging in hands-on activities to select random samples and to compare samples of different sizes.

## Unit Summary

In Unit 7, seventh-grade students investigate how they can use sampling to make inferences about larger populations of interest. They begin the unit by understanding that random sampling tends to produce the most representative and “fair” samples and that the size of the sample can make a difference in the accuracy of predictions and the variability of results. Students engage in hands-on activities to select random samples and to compare samples of different sizes. Students also calculate measures of center and variability of samples, most notably, the mean and the mean absolute deviation, or MAD, and use these measures to compare across different populations (MP.2). Throughout the unit, students reason about data, make connections, and defend their reasoning by constructing arguments (MP.3). Students also re-engage in the major work of the grade, particularly their work with ratios and proportions, when they use proportional reasoning to estimate population characteristics based on sample statistics.

In sixth grade, students began their study of statistics by understanding what makes a statistical question. They studied shapes of distributions of data and calculated measures of center and spread. Students made connections between the data and the contexts they represented, ensuring the numerical aspects of statistics were not separated from the statistical question that drove the analysis. All of these understandings will support seventh-grade students in their work in this unit.

In eighth grade, students will shift to study patterns of association in bivariate data. They will collect data to represent two categorical variables and analyze the results to determine if there are associations or tendencies between the variables. Later in high school, students will delve deeply into statistics and, using their understanding of mean and MAD, they will use mean and standard deviation to fit data to normal distributions.

Note: In the CCSSM, the concept of MAD is first introduced in sixth grade. In the Massachusetts Frameworks, MAD is first introduced in seventh grade. This unit follows the MA Frameworks and therefore assumes that students have not had prior experience with MAD.

Pacing: 11 instructional days (9 lessons, 1 flex day, 1 assessment day)

For guidance on adjusting the pacing for the 2020-2021 school year due to school closures, see our 7th Grade Scope and Sequence Recommended Adjustments.

• Expanded Assessment Package
• Problem Sets for Each Lesson
• Student Handout Editor
• Vocabulary Package

## Assessment

This assessment accompanies Unit 7 and should be given on the suggested assessment day or after completing the unit.

## Unit Prep

### Intellectual Prep

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#### Internalization of Standards via the Unit Assessment

• Take unit assessment. Annotate for:
• Standards that each question aligns to
• Strategies and representations used in daily lessons
• Relationship to Essential Understandings of unit
• Lesson(s) that assessment points to

#### Internalization of Trajectory of Unit

• Read and annotate "Unit Summary."
• Notice the progression of concepts through the unit using “Unit at a Glance.”
• Essential understandings
• Connection to assessment questions
• Identify key opportunities to engage students in academic discourse. Read through our Guide to Academic Discourse and refer back to it throughout the unit.

### Essential Understandings

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• Studying sample statistics is a way to reasonably understand and make predictions about larger population characteristics.
• Random samples tend to produce the most representative samples of populations. The larger the sample size, the more accurate and less variable the data tends to be.
• Sample data can be used to compare characteristics of interest between two or more populations. The mean and mean absolute deviation can shed light on differences between populations and how meaningful these differences are compared to sampling variability.

### Vocabulary

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distribution

population characteristic

statistical question

population

sample population

sample statistic

sample proportion

representative sample

random sample

measure of center

population proportion

mean (average)

range

interquartile range

### Unit Materials, Representations and Tools

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• Dot plots
• Box plots
• Calculators
• Random number generator
• Brown bags with cubes
• Brown bags with numbers
• Decks of playing cards

## Common Core Standards

Key: Major Cluster Supporting Cluster Additional Cluster

### Core Standards

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##### Statistics and Probability
• 7.SP.A.1 — Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

• 7.SP.A.2 — Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.

• 7.SP.B.3 — Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.

• 7.SP.B.4 — Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.

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• 6.SP.A.1

• 6.SP.A.2

• 6.SP.A.3

• 6.SP.B.4

• 6.SP.B.5

• 6.SP.B.5.C

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• HSS-ID.A.2

• HSS-ID.A.3

• HSS-ID.A.4

• HSS-IC.A.1

• HSS-IC.B.4

• 8.SP.A.4

### Standards for Mathematical Practice

• CCSS.MATH.PRACTICE.MP1 — Make sense of problems and persevere in solving them.

• CCSS.MATH.PRACTICE.MP2 — Reason abstractly and quantitatively.

• CCSS.MATH.PRACTICE.MP3 — Construct viable arguments and critique the reasoning of others.

• CCSS.MATH.PRACTICE.MP4 — Model with mathematics.

• CCSS.MATH.PRACTICE.MP5 — Use appropriate tools strategically.

• CCSS.MATH.PRACTICE.MP6 — Attend to precision.

• CCSS.MATH.PRACTICE.MP7 — Look for and make use of structure.

• CCSS.MATH.PRACTICE.MP8 — Look for and express regularity in repeated reasoning.