Unit 8: Statistics
Students get their first experience of statistics in this unit, defining a statistical question and investigating the key concepts of measures of center and measures of variability.
In Unit 8, sixth graders get their first experience of statistics. Students come into sixth grade with some prior knowledge around data representations, such as bar graphs and line plots; however, this is the first time that students ask the question “what is statistics” and “what can it help me solve?” Students begin the unit by first determining what a statistical question is. Then they ask how they can interpret the data that comes from these questions (MP.2). Students learn various ways to represent the data, including frequency tables, histograms, dot plots, box plots, and circle graphs, and they analyze each representation to determine what information and conclusions they can glean from each one (MP.4).
Students will investigate two key concepts that will be important for future studies: measures of center and measures of variability. They’ll look at measures of center to investigate what a “typical” or average response to a question might be; they’ll look at measures of variation to understand how similar or different the data in the set may be or how reliable a measure of center might be. Students investigate all of this within context in order to better understand how statistics can be used to investigate questions and understand more about our world.
In seventh grade, students will continue their study of statistics and investigate multiple data distributions simultaneously. They will also deepen their understanding of sampling and how to use random sampling to draw inferences about populations.
Note: In December 2022, this unit was revised slightly to align more closely to the Common Core State Standards for Mathematics (CCSSM). The revision involved shifting when the concept of mean absolute deviation (MAD) was introduced from seventh grade to sixth grade. As a result, this unit now includes a new lesson (Lesson 10) where students understand MAD as a measure of variability of a data set. Students continue their work with measures of variability, including MAD, in seventh grade Unit 7.
Pacing: 16 instructional days (14 lessons, 1 flex day, 1 assessment day)
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The following assessments accompany Unit 8.
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.
Pre-Unit Student Self-Assessment
Have students complete the Mid-Unit Assessment after lesson 7.
Use the resources below to assess student mastery of the unit content and action plan for future units.
Post-Unit Assessment Answer Key
Post-Unit Student Self-Assessment
Use student data to drive your planning with an expanded suite of unit assessments to help gauge students’ facility with foundational skills and concepts, as well as their progress with unit content.
Suggestions for how to prepare to teach this unit
The central mathematical concepts that students will come to understand in this unit
Terms and notation that students learn or use in the unit
measure of center
To see all the vocabulary for Unit 8, view our 6th Grade Vocabulary Glossary.
The materials, representations, and tools teachers and students will need for this unit
To see all the materials needed for this course, view our 6th Grade Course Material Overview.
Topic A: Understanding Statistics & Distributions
Define and identify statistical questions.
Describe data that is represented in a dot plot. Represent data using dot plots and frequency tables.
Represent data using histograms.
Describe and analyze the overall shape of dot plots and histograms, including symmetry, skewness, outliers, and clusters.
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Topic B: Measurements of Center & Variability
Define and determine the mean of a data set.
Define and determine the median of a data set.
Define and determine the mode of a data set.
Determine which measure of center best represents a data set. Determine how measures of center change when data is added or removed.
Use the range and interquartile range to understand the spread and variability of a data set.
Understand and determine mean absolute deviation (MAD) as a measure of variability of a data set.
Compare measures of center and measures of spread to describe data sets.
Topic C: Box Plots & Circle Graphs
Represent data using box plots.
Analyze box plots and other representations, and summarize numerical data in context.
Analyze circle graphs in context.
The content standards covered in this unit
— 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.
— 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.
— 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.
— Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
— Summarize numerical data sets in relation to their context, such as by:
— Reporting the number of observations.
— Describing the nature of the attribute under investigation, including how it was measured and its units of measurement.
— 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.
— Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.
Standards covered in previous units or grades that are important background for the current unit
— Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.
— Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement:
— Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.
For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.
— Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
— Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
— Fluently divide multi-digit numbers using the standard algorithm.
— Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Standards in future grades or units that connect to the content in this unit
— Represent data with plots on the real number line (dot plots, histograms, and box plots).
— 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.
— Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
— 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.
— 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.
— 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.
— 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.
— 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.
— Make sense of problems and persevere in solving them.
— Reason abstractly and quantitatively.
— Construct viable arguments and critique the reasoning of others.
— Model with mathematics.
— Use appropriate tools strategically.
— Attend to precision.
— Look for and make use of structure.
— Look for and express regularity in repeated reasoning.