MA.7.DP.1.2

Given two numerical or graphical representations of data, use the measure(s) of center and measure(s) of variability to make comparisons, interpret results and draw conclusions about the two populations.

Clarifications

Clarification 1: Graphical representations are limited to histograms, line plots, box plots and stem-and-leaf plots.

Clarification 2: The measure of center is limited to mean and median. The measure of variation is limited to range and interquartile range.

General Information
Subject Area: Mathematics (B.E.S.T.)
Strand: Data Analysis and Probability
Status: State Board Approved

Benchmark Instructional Guide

Terms from the K-12 Glossary

• Box Plot
• Data
• Histogram
• Interquartile Range (IQR)
• Line Plot
• Mean
• Measures of Center
• Measures of Variability
• Median
• Range (of data set)
• Stem-and-Leaf Plot

Vertical Alignment

Previous Benchmarks

Next Benchmarks

Purpose and Instructional Strategies

In grade 6, students calculated and interpreted mean, median, mode and range, while in grade 7, they use those calculations to make comparisons, interpret results and draw conclusions about two populations. In grade 8, students will learn how to interpret the main features of line graphs and lines of fit.
• Instruction includes cases where students need to calculate measures of center and variation in order to interpret them.
• Instruction includes having students collect their own data for analysis. Student interest in making comparisons assists with students making sense of the data to interpret comparisons (MTR.1.1, MTR.7.1).
• Students should not be expected to classify differences between data sets as “significant” or “not significant.”
• Data representations can be shown as a two-sided stem-and-leaf plot and multiple box plots on the same scale.
• Data representations should include titles, labels and a key as appropriate.

Common Misconceptions or Errors

• Some students may incorrectly believe a histogram with greater variability in the heights of the bars indicates greater variability of the data set.
• Students may not recognize when to use a stem-and-leaf plot or may not be able to read a two-sided stem-and-leaf plot.
• Students may not be able to explain their choice of the most appropriate measures of center and variability based on the given data.
• Students may think that the presence of one or more outliers leads to an automatic choice (median, IQR) for the measures of center and variation.

Strategies to Support Tiered Instruction

• Instruction includes explaining the difference between variability in the heights of the bars of histograms, and the actual variability of the data set.
• Teacher provides instruction on how to use different type of data displays to show two sets of data at the same time. Teachers co-construct an anchor chart explaining the different parts of each display with explanations on when and how to use each of them.
• For example, teacher can provide students with a two-sided stem-and-leaf plot with the “stem” in the middle and “leaves” on either side, each displaying the two data sets.

• For example, teacher can provide students with two line plots or two box plots on the same number line. Plots can be given in different colors to show the different data sets.
• Teacher provides instruction on which measure of center and variation should be used, making sure to include what to do when an outlier is present.
• Teacher facilitates discussion on the different measures of center and variability and how to know when to use each one. Use a graphic organizer to compare the different measures of center and variability to assist students in deciding when to use them.
• Instruction includes co-creating an anchor chart with different data displays containing visual representations and explanations of when and how to use them.

A group of students in the book club are debating whether high school juniors or seniors spend more time on homework. A random sampling of juniors and seniors at the local high school were surveyed about the average amount of time they spent per night on homework. The results are listed in the table below.
Average Amount of Time on Homework Per Night (in minutes)

• Part A. Calculate and compare the measures of center for the data sets.
• Part B. Calculate and compare the variability in each distribution.
• Part C. Does the data support juniors or seniors spending more time on homework? Explain your reasoning.

Instructional Items

Instructional Item 1
High schools around the state of Florida were asked what percentage of students in their graduating class would be attending a state college and what percentage would be attending a community college. The results are provided in the graph below.

Is a student more likely to go to a state or community college? Which choice has more variability?

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1205020: M/J Accelerated Mathematics Grade 6 (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022, 2022 and beyond (current))
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.7.DP.1.AP.2: Given two numerical or graphical representations of data in the same form, compare the mean, median or range of each representation.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Formative Assessments

Cranberry Counting:

Students are asked to assess the validity of an inference regarding two distributions given their box plots.

Type: Formative Assessment

TV Ages - 1:

Students are asked to informally determine the degree of overlap between two distributions with the same interquartile range (IQR) by expressing the difference between their medians as a multiple of the IQR.

Type: Formative Assessment

TV Ages - 2:

Students are asked to informally determine the degree of overlap between two distributions with the same interquartile range (IQR) by expressing the difference between their medians as a multiple of the IQR.

Type: Formative Assessment

Overlapping Trees:

Students are asked to compare two distributions given side-by-side box plots.

Type: Formative Assessment

Lesson Plans

A MEANingful Discussion about Central Tendency:

Using relatable scenarios, this lesson explores the mean and median of a data set and how an outlier affects each measure differently.

Type: Lesson Plan

Students will utilize historical trade flow data (import and export) to interpret, create, and draw conclusions about foreign policy, specifically the World Trade Organization. Students will write a claim using the data to make suggestions regarding foreign trade import and export in this integrated lesson plan.

Type: Lesson Plan

Build a New School:

Students will calculate, interpret, and use measures of center and spread of different populations to determine in which city in Manatee County new schools should be built. Students will also use percentages to estimate the future population of school-aged children which will be used to determine where new schools should be built.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here: https://www.cpalms.org/cpalms/mea.aspx to learn more about MEAs and how they can transform your classroom.They resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. MEAs follow a problem-based, student centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator.

Type: Lesson Plan

Measurement Data Error:

In this interdisciplinary lesson, students will practice the skill of data collection with a variety of tools and by statistically analyzing the class data sets will begin to understand that error is inherent in all data.

Type: Lesson Plan

Analyzing Box Plots:

This lesson is designed for students to demonstrate their knowledge of box plots.

• Students will need to create four box plots from given data.
• Students will need to analyze the data displayed on the box plots by comparing similarities and differences.
• Students will work with a partner to complete the displays and the follow-up questions.

Type: Lesson Plan

Students will compile the data gathered from measuring their resting heart rates and heart rates after exercising into box plots. Using these displays, they will analyze the data's center, shape, and spread.

Type: Lesson Plan

Bowling for Box Plots:

Students will learn about the effects of an outlier and interpret differences in shape, center, and spread using a bowling activity to gather data. The students will learn to score their games, report their scores, and collectively measure trends and spread by collaborating to create a box plot. They will analyze and compare box plots, and determine how much of an effect an extreme score (outlier) can have on the overall box plot of the data.

Type: Lesson Plan

How tall is an 8th grader?:

Ever wonder about the differences in heights between students in grade 8? In this lesson, students will use data they collect to create and analyze multiple box plots using 5-number summaries. Students will make inferences about how height and another category may or may not be related.

Type: Lesson Plan

Plane Statistics:

This lesson starts with an activity to gather data using paper airplanes then progresses to using appropriate statistics to compare the center and spread of the data. Box plots are used in this application lesson of concepts and skills previously acquired.

Type: Lesson Plan

This resource can be used to teach students how to create and compare box plots. After completing this lesson, students should be able to answer questions in both familiar and unfamiliar situations.

Type: Lesson Plan

The Distance a Coin Will Travel:

This lesson is a hands-on activity that will allow students to collect and display data about how far different coins will travel. The data collected is then used to construct double dot plots and double box plots. This activity helps to facilitate the statistical implications of data collection and the application of central tendency and variability in data collection.

Type: Lesson Plan

Which is Better? Using Data to Make Choices:

Students use technology to analyze measures of center and variability in data. Data displays such as box plots, line plots, and histograms are used. The effects of outliers are taken into consideration when drawing conclusions. Students will cite evidence from the data to support their conclusions.

Type: Lesson Plan

How long did you study?:

Students will create and analyze histograms based on student study time when preparing for the Algebra EOC. Students will be given a set of data and guided notes

Type: Lesson Plan

How many licks does it take to get to the center?:

Students will create different displays, line plots, histograms, and box plots from data collected about types of lollipops. The data will be analyzed and compared. Students will determine "Which lollipop takes the fewest number of licks to get to the center: a Tootsie Pop, a Blow Pop, or a Dum Dum?"

Type: Lesson Plan

Birthday Party Decisions:

Students will create and compare four different boxplots to determine the best location for a birthday party.

Type: Lesson Plan

Outliers in the Outfield – Dealing With Extreme Data Points:

Students will explore the effects outliers have on the mean and median values using the Major League Baseball (MLB) salary statistics. They will create and compare box plots and analyze measures of center and variability. They will also be given a set of three box plots and asked to identify and compare their measures of center and variablity.

Type: Lesson Plan

This lesson allows students to have a hands-on experience collecting real-world data, creating graphical representations, and analyzing their data. Students will make predictions as to the outcome of the data and compare their predictions to the actual outcome. Students will create and analyze line plots, histograms, and box plots.

Type: Lesson Plan

Comparing Data Using Box Plots:

Students will use box plots to compare two or more sets of data. They will analyze data in context by comparing the box plots of two or more data sets.

Type: Lesson Plan

Digging the Plots:

Students construct box plots and use the measure(s) of center and variability to make comparisons, interpret results, and draw conclusions about two populations.

Type: Lesson Plan

A Walk Down the Lane:

Students will collect data, and create box plots. Students will make predictions about which measurement best describes the spread and center of the data. Students will use this information to make predictions.

Type: Lesson Plan

How Old are the Players?:

For this lesson, students will research the ages of players on two basketball teams. They will find the five-number summary, the mean, and determine if there are outliers in the data set. Two box plots will be created and the measures of center and variation analyzed.

Type: Lesson Plan

The students will compare the effects of outliers on measures of center and spread within dot plots and box plots.

Type: Lesson Plan

Baking Soda and Vinegar: A statistical approach to a chemical reaction.:

Students experiment with baking soda and vinegar and use statistics to determine which ratio of ingredients creates the most carbon dioxide. This hands-on activity applies the concepts of plot, center, and spread.

Type: Lesson Plan

Should Statistics be Shapely?:

Students will Interpret differences in shape, center, and spread of a variety of data displays, accounting for possible effects of extreme data points.

Students will create a Human Box Plot using their data to master the standard and learning objectives, then complete interactive notes with the classroom teacher, a formative assessment, and later a summative assessment to show mastery.

Type: Lesson Plan

Is My Backpack Too Massive?:

This lesson combines many objectives for seventh grade students. Its goal is for students to create and carry out an investigation about student backpack mass. Students will develop a conclusion based on statistical and graphical analysis.

Type: Lesson Plan

Exploring Box plots:

This lesson involves real-world data situations. Students will use the data to create, explore, and compare the key components of a box plot.

Type: Lesson Plan

The Debate: Who is a Better Baller?:

In this activity the students will use NBA statistics on Lebron James and Tim Duncan who were key players in the 2014 NBA Finals, to calculate, compare, and discuss mean, median, interquartile range, variance, and standard deviation. They will also construct and discuss box plots.

Type: Lesson Plan

Who's Better?--Using Data to Determine:

This lesson is intended for use after students are able to construct data plots (histograms, line plots, box plots). Students are tasked with not only constructing data plots, but also matching data plots to data sets. In the summative assessment, students are given two data sets and asked to select which of three data plots (histogram, line plot, or box plot) would best be used to compare the data. After choosing and constructing their plot, students are then tasked with forming a conclusion based on the plots they have constructed.

Type: Lesson Plan

Burgers to Smoothies.:

Students will create double box plots to compare nutritional data about popular food choices.

Type: Lesson Plan

A MEANingful Discussion about Central Tendency:

Using relatable scenarios, this lesson explores the mean and median of a data set and how an outlier affects each measure differently.

Type: Lesson Plan

Original Student Tutorial

Math Models and Social Distancing:

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Experts

Chronic Pain and the Brain:

<p>Florida State researcher Jens Foell discusses the use of fMRI&nbsp;and statistics in chronic pain.</p>

Type: Perspectives Video: Expert

fMRI, Phantom Limb Pain and Statistical Noise:

<p>Jens Foell&nbsp;discusses how statistical noise reduction is used in fMRI&nbsp;brain imaging to be able to determine which specifics parts of the brain are related to certain activities and how this relates to patients that suffer from phantom limb pain.</p>

Type: Perspectives Video: Expert

Histograms Show Trends in Fisheries Data Over Time:

<p>NOAA Fishery management relies on histograms to show patterns and trends over time of fishery data.</p>

Type: Perspectives Video: Expert

Mathematically Exploring the Wakulla Caves:

The tide is high! How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Nestle Waters & Statistical Analysis:

<p>Hydrogeologist&nbsp;from Nestle Waters discusses the importance&nbsp;of statistical tests in monitoring&nbsp;sustainability and in maintaining consistent&nbsp;water quality in bottled water.</p>

Type: Perspectives Video: Professional/Enthusiast

Statistical Art: Four Words:

<p>Graphic designer and artist,&nbsp;Drexston&nbsp;Redway&nbsp;infuses statistics into his artwork to show population distribution and overlap of poverty and ethnicity in Tallahassee, FL.</p>

Type: Perspectives Video: Professional/Enthusiast

Camera versus Trap Sampling: Improving how NOAA Samples Fish :

<p>Underwater sampling with cameras has made fishery management more accurate for NOAA&nbsp;scientists.</p>

Type: Perspectives Video: Professional/Enthusiast

Sampling Amphibian Populations to Study Human Impact on Wetlands:

<p>Ecologist Rebecca Means discusses the use of statistical sampling and comparative studies in field biology.</p>

Type: Perspectives Video: Professional/Enthusiast

Mean Data and Striking Deviations in Sea Turtle Research:

<p>Dive in and learn about how statistics can be used to help research sea turtles!</p>

Type: Perspectives Video: Professional/Enthusiast

Statistical Analysis of a Randomized Study:

<p>This education researcher uses measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.</p>

Type: Perspectives Video: Professional/Enthusiast

Perspectives Video: Teaching Ideas

Using Visual Models to Determine Mode, Median and Range:

Unlock an effective teaching strategy for teaching median, mode, and range in this Teacher Perspectives Video for educators.

Type: Perspectives Video: Teaching Idea

Atlatl - Differences in Velocity and Distance:

<p>An archaeologist describes how an ancient weapons technology can be used to bring home dinner or generate data for a math lesson.</p>

Type: Perspectives Video: Teaching Idea

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Offensive Linemen:

In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale.

Teaching Idea

Pump Up the Volume:

This activity is a statistical analysis of recorded measurements of a single value - in this case, a partially filled graduated cylinder.

Type: Teaching Idea

MFAS Formative Assessments

Cranberry Counting:

Students are asked to assess the validity of an inference regarding two distributions given their box plots.

Overlapping Trees:

Students are asked to compare two distributions given side-by-side box plots.

TV Ages - 1:

Students are asked to informally determine the degree of overlap between two distributions with the same interquartile range (IQR) by expressing the difference between their medians as a multiple of the IQR.

TV Ages - 2:

Students are asked to informally determine the degree of overlap between two distributions with the same interquartile range (IQR) by expressing the difference between their medians as a multiple of the IQR.

Original Student Tutorials Mathematics - Grades 6-8

Math Models and Social Distancing:

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorial

Math Models and Social Distancing:

Learn how math models can show why social distancing during a epidemic or pandemic is important in this interactive tutorial.

Type: Original Student Tutorial

Perspectives Video: Expert

Mathematically Exploring the Wakulla Caves:

The tide is high! How can we statistically prove there is a relationship between the tides on the Gulf Coast and in a fresh water spring 20 miles from each other?

Type: Perspectives Video: Expert

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.

Haircut Costs:

This problem could be used as an introductory lesson to introduce group comparisons and to engage students in a question they may find amusing and interesting.

Offensive Linemen:

In this task, students are able to conjecture about the differences and similarities in the two groups from a strictly visual perspective and then support their comparisons with appropriate measures of center and variability. This will reinforce that much can be gleaned simply from visual comparison of appropriate graphs, particularly those of similar scale.

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Speed Trap:

The purpose of this task is to allow students to demonstrate an ability to construct boxplots and to use boxplots as the basis for comparing distributions.