MAFS.7.SP.2.3

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.
General Information
Subject Area: Mathematics
Grade: 7
Domain-Subdomain: Statistics & Probability
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Draw informal comparative inferences about two populations. (Additional Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Date of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

    Assessed with: 

    MAFS.7.SP.2.4 


Sample Test Items (1)
  • Test Item #: Sample Item 1
  • Question:

    Two classes have a trivia contest. Each student is asked eight questions and is scored on the number of correct answers. The teachers create a dot plot of the scores from 15 students from Class A and 14 students from Class B, as shown.

    Another score is added to the plot for Class B to make the median of the two data sets equal.

    Click on the dot plot to show where this score could have been added.

  • Difficulty: N/A
  • Type: GRID: Graphic Response Item Display

Related Courses

This benchmark is part of these courses.
1205040: M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205050: M/J Grade 7 Accelerated Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2020, 2020 - 2022 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
7812020: Access M/J Grade 7 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2019, 2019 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.7.SP.2.AP.3a: Given graphed distributions of two sets of data, make statements comparing the two sets of data.

Related Resources

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

Assessments

Sample 4 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Sample 2 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Formative Assessments

Comparing Test Scores:

Students are asked to informally determine the degree of overlap between two distributions with the same mean absolute deviation (MAD) by expressing the difference in their means as a multiple of the MAD.

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

Lesson Plans

Sea Ice Analysis Grade 7:

The changing climate is an important topic for both scientific analysis and worldly knowledge. This lesson uses data collected by the National Snow and Ice Data Center to create and use statistical analysis as a tool to evaluate the sea ice loss. Students will use technology to quickly generate graphs for each month looking for trends, patterns, or deviations over time.

Type: Lesson Plan

Sensoring Data:

In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.

Type: Lesson Plan

Measurement and Data Collection:

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.

This lesson uses the Hip Sciences Sensor Wand and Temperature Probe. Please refer to the corresponding Hip Science Sensor Guide(s) for information on using the sensor.

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

Measurement and Data Collection:

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.

This lesson uses the Hip Sciences Sensor Wand and Temperature Probe. Please refer to the corresponding Hip Science Sensor Guide(s) for information on using the sensor.

Type: Lesson Plan

Sensoring Data:

In this follow up lesson, students will explore data collection using the weather station sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation of their own. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a personally meaningful way.

Type: Lesson Plan

Hot Coffee Coming Through:

In this lesson, students will explore data collection using the temperature probe sensor and perform statistical analysis of the data. Students will use a scientific method of inquiry to plan an investigation to determine which coffee mug is the best. This activity is meant to allow students to use a variety of skills they have acquired throughout a statistics unit in a problem based STEM challenge. Due to the multiple skills there are many standards that are covered.

There are two options for this lab. The first student handout is for students at an average high school statistics level (Algebra 1) and will allow for standard deviation and graphical analyses of the data. The second option is for advanced students that have been exposed to hypothesis testing of claims (Algebra 2 or AP Stats).

Type: Lesson Plan

Stepping Up Measures of Center:

This lesson allows for students to explore the use of dot plots and mean absolute deviation to compare and draw inferences from two different sets of numerical data.

Type: Lesson Plan

Grapevine Fabrication Part 2:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to collect data to perform basic statistical operations to analyze and make comparisons on variability within a certain brand of raisins. Part 1 must be completed prior to starting Part 2. This investigation can elicit discussion about manufacturing and quality control.

Type: Lesson Plan

Bubble Gum Bubbles Lab:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to collect data by blowing bubble gum bubbles and perform statistical analysis, including standard deviation. This lesson provides students an applied setting to use their previously acquired statistical skills.

Type: Lesson Plan

Height Arm Juxtaposition:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to apply their skills on analyzing bivariate data. This STEM lesson allows students the opportunity to investigate if there is a linear relationship between a person's height and arm length. Using technology the students will explore in-depth how to perform a least square regression as a procedure for determining the line of best fit.

Type: Lesson Plan

Grapevine Fabrication Part 1:

This lesson is a Follow Up Activity to the Algebra Institute and allows students to collect data to perform basic statistical operations to analyze and make comparisons on variability within a certain brand of raisins. Part 1 may be completed without Part 2. This investigation can elicit discussion about manufacturing and quality control.

Type: Lesson Plan

Is My Backpack Too Heavy?:

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

Type: Lesson Plan

Who's Taller?:

This lesson uses real-world data sets to guide students through representing and comparing data sets in separate dot plots. Students will represent and compare the data sets by using the mean and MAD (mean absolute deviation).

Type: Lesson Plan

Likely Events: Which Bag is It?:

The resource is complete, containing standards, assessments, prior knowledge, objectives, a lesson plan, and a spreadsheet that simulates experiments in which objects are drawn with replacement from each of two bags. Students will try to make sense out of the sampled results of both physical and computer simulated experiments. They will indicate an increased confidence in their inferences as the number of trials increases.

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:

Florida State researcher Jens Foell discusses the use of fMRI and statistics in chronic pain.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

fMRI, Phantom Limb PainĀ and Statistical Noise:

Jens Foell discusses how statistical noise reduction is used in fMRI 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.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Histograms Show Trends in Fisheries Data Over Time:

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

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Expert

Perspectives Video: Professional/Enthusiasts

Statistical Art: Four Words:

Graphic designer and artist, Drexston Redway infuses statistics into his artwork to show population distribution and overlap of poverty and ethnicity in Tallahassee, FL.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Sampling Amphibian Populations to Study Human Impact on Wetlands:

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

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Perspectives Video: Teaching Idea

Atlatl - Differences in Velocity and Distance:

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

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Teaching Idea

Problem-Solving Tasks

Bear Hugs:

In this problem solving activity, students are tasked with measuring the arm lengths of fellow students. Students will record the data and use it to construct a boxplot and scatterplot to help draw conclusions.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Virtual Manipulatives

Box Plot:

In this activity, students use preset data or enter in their own data to be represented in a box plot. This activity allows students to explore single as well as side-by-side box plots of different data. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

Type: Virtual Manipulative

Advanced Data Grapher:

This is an online graphing utility that can be used to create box plots, bubble graphs, scatterplots, histograms, and stem-and-leaf plots.

Type: Virtual Manipulative

Box Plotter:

Users select a data set or enter their own data to generate a box plot.

Type: Virtual Manipulative

Exploring Mean and Median Using Box Plots:

Using an interactive applet, students can compare and contrast properties of measures of central tendency, specifically the influence of changes in data values on the mean and median. As students change the data values by dragging the red points to the left or right, the interactive figure dynamically adjusts the mean and median of the new data set.
(NCTM's Illuminations)

Type: Virtual Manipulative

MFAS Formative Assessments

Comparing Test Scores:

Students are asked to informally determine the degree of overlap between two distributions with the same mean absolute deviation (MAD) by expressing the difference in their means as a multiple of the MAD.

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

Problem-Solving Task

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.

Type: Problem-Solving Task

Virtual Manipulatives

Box Plot:

In this activity, students use preset data or enter in their own data to be represented in a box plot. This activity allows students to explore single as well as side-by-side box plots of different data. This activity includes supplemental materials, including background information about the topics covered, a description of how to use the application, and exploration questions for use with the Java applet.

Type: Virtual Manipulative

Advanced Data Grapher:

This is an online graphing utility that can be used to create box plots, bubble graphs, scatterplots, histograms, and stem-and-leaf plots.

Type: Virtual Manipulative

Box Plotter:

Users select a data set or enter their own data to generate a box plot.

Type: Virtual Manipulative

Exploring Mean and Median Using Box Plots:

Using an interactive applet, students can compare and contrast properties of measures of central tendency, specifically the influence of changes in data values on the mean and median. As students change the data values by dragging the red points to the left or right, the interactive figure dynamically adjusts the mean and median of the new data set.
(NCTM's Illuminations)

Type: Virtual Manipulative

Parent Resources

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

Problem-Solving Task

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.

Type: Problem-Solving Task