Math / 7th Grade / Unit 7: Statistics

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.

Math

Unit 7

7th Grade

Unit Summary

Please Note: In January 2026, this unit and its lesson plans received a round of enhancements. Teachers should pay close attention as they intellectually prepare to account for the updated pacing and content.

In Unit 7, 7th 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 Reason abstractly and quantitatively. . Throughout the unit, students reason about data, make connections, and defend their reasoning by constructing arguments MP.3 Construct viable arguments and critique the reasoning of others. . 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 6th 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, including the mean absolute deviation. 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 7th grade students in their work in this unit.

In 8th 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.

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

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Assessment

The following assessments accompany Unit 7.

Pre-Unit

Have students complete the Pre-Unit Assessment and Pre-Unit Student Self-Assessment before starting the unit. Use the Pre-Unit Assessment Analysis Guide to identify gaps in foundational understanding and map out a plan for learning acceleration throughout the unit.

Mid-Unit

Have students complete the Mid-Unit Assessment after Lesson 4.

Post-Unit

Use the resources below to assess student understanding of the unit content and action plan for future units.

Expanded Assessment Package

Use student data to drive instruction with an expanded suite of assessments. Unlock Pre-Unit and Mid-Unit Assessments, and detailed Assessment Analysis Guides to help assess foundational skills, progress with unit content, and help inform your planning.

Unit Prep

Intellectual Prep

Suggestions for how to prepare to teach this unit

Internalization of Standards via the Post-Unit Assessment

Take the Post-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 the Unit Summary.
Notice the progression of concepts through the unit using the Lesson Map.
Do all Target Tasks. Annotate the Target Tasks for:
- Essential Understandings
- Connection to Post-Unit Assessment questions
Identify key opportunities to engage students in academic discourse. Read through our Teacher Tool on Academic Discourse and refer back to it throughout the unit.

Unit-Specific Intellectual Prep

Read the Progressions for the Common Core State Standards in Mathematics, 6-8 Statistics and Probability for standards relevant to this unit.

Essential Understandings

The central mathematical concepts that students will come to understand in this unit

Studying sample statistics allows us to make reasonable claims and predictions about larger population characteristics, even when we cannot measure the entire population.
Random samples are more likely to be representative of a population, and larger sample sizes tend to reduce variability, making sample statistics more reliable indicators of population characteristics.
Sample data can be used to compare characteristics of two or more populations. The mean and mean absolute deviation help us evaluate whether observed differences are meaningful relative to the variability in the data.

Vocabulary

Terms and notation that students learn or use in the unit

Unit Vocabulary

bias

population proportion

population characteristic

population

random sample

representative

sample distribution

sampling methods

sample population

sample statistic

sample proportion

unrepresentative sample

valid

Foundational Vocabulary

distribution

interquartile range

measure of center

mean absolute deviation (MAD)

mean (average)

range

statistical question

To see all the vocabulary for Unit 7, view our 7th Grade Vocabulary Glossary.

Access foundational vocabulary for Unit 7 in the same 7th Grade Vocabulary Glossary.

Materials

The materials, representations, and tools teachers and students will need for this unit

Calculators (1 per student)
Brown bag (1 per small group)
Cubes (1 set per small group) — 5 blue cubes and 15 of any other color
Roosevelt Middle School Survey (1 per pair)
Counting Trees Worksheet (1 per pair)
Computers or Tablets (1 per student group)
Simulated Media Representation Data Set — Student will need digital access to material
Random Number Slides
Abuelito Who (1 per student)
Table of Random Digits (1 per pair)
Slow Reveal Dot Plots
Heights and Weights Data Sets
Unit 7 Project - Teacher Guide

To see all the materials needed for this course, view our 7th Grade Course Material Overview.

Lesson Map

Topic A: Understanding Populations and Samples

Lesson

Understand and identify populations and sample populations for statistical questions.

Standards

7.SP.A.1

Lesson

Describe sampling methods that result in representative samples.

Standards

7.SP.A.1

Lesson

Generate a random sample for a statistical question.

Standards

7.SP.A.17.SP.A.2

Topic B: Using Sample Data to Draw Inferences About a Population

Lesson

Analyze data sets using measures of center and measures of variability.

Standards

7.SP.B.37.SP.B.4

Lesson

Determine the impact of sample size on variability and prediction accuracy.

Standards

7.SP.A.2

Lesson

Estimate population proportions using sample data.

Standards

7.SP.A.2

Topic C: Using Sample Data to Compare Two or More Populations

Lesson

Compare different populations by analyzing visual data distributions.

Standards

7.SP.B.37.SP.B.4

Lesson

Compare populations by analyzing numerical data.

Standards

7.SP.B.37.SP.B.4

Lesson

Identify meaningful differences between populations using the mean and mean absolute deviation (MAD) of samples.

Standards

7.SP.B.37.SP.B.4

Common Core Standards

Key

Major Cluster

Supporting Cluster

Additional Cluster

Core Standards

The content standards covered in this unit

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.

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.

Statistics and Probability

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.

Statistics and Probability

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.

Statistics and Probability

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.

Foundational Standards

Standards covered in previous units or grades that are important background for the current unit

Statistics and Probability

6.SP.A.1

Statistics and Probability

6.SP.A.1 — Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question because one anticipates variability in students' ages.
6.SP.A.2

Statistics and Probability

6.SP.A.2 — Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.A.3

Statistics and Probability

6.SP.A.3 — Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
6.SP.B.4

Statistics and Probability

6.SP.B.4 — Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.B.5

Statistics and Probability

6.SP.B.5 — Summarize numerical data sets in relation to their context, such as by:
6.SP.B.5.C

Statistics and Probability

6.SP.B.5.C — Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

Future Standards

Standards in future grades or units that connect to the content in this unit

Interpreting Categorical and Quantitative Data

HSS-ID.A.2

Interpreting Categorical and Quantitative Data

HSS-ID.A.2 — Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
HSS-ID.A.3

Interpreting Categorical and Quantitative Data

HSS-ID.A.3 — Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
HSS-ID.A.4

Interpreting Categorical and Quantitative Data

HSS-ID.A.4 — Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Making Inferences and Justifying Conclusions

HSS-IC.A.1

Making Inferences and Justifying Conclusions

HSS-IC.A.1 — Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
HSS-IC.B.4

Making Inferences and Justifying Conclusions

HSS-IC.B.4 — Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

Statistics and Probability

8.SP.A.4

Statistics and Probability

8.SP.A.4 — Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?

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.

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