MAFS.7.SP.2.4

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.
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
    Also Assesses:

    MAFS.7.SP.2.3

  • Assessment Limits :

    N/A

  • Calculator :

    Neutral

  • Context :

    Required

Sample Test Items (2)
  • Test Item #: Sample Item 1
  • Question:

    Box plots for chapter 6 test scores of two classes are shown.

     

    What is the difference in the median between the two sets of data?




     

  • Difficulty: N/A
  • Type: EE: Equation Editor

  • Test Item #: Sample Item 2
  • Question:

    Survey data involving two random samples of students at a law school are shown. The surveys were taken comparing the age of students in 1990 to the age of students in 2014.

    Select all the statements that are true about the two samples of students.

     

  • Difficulty: N/A
  • Type: SHT: Selectable Hot Text

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)
2002050: M/J Comprehensive Science 1, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2002070: M/J Comprehensive Science 2 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2002080: M/J Comprehensive Science 2, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2001020: M/J Earth/Space Science, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2000020: M/J Life Science, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2003010: M/J Physical Science (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)
2003020: M/J Physical Science, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022, 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)
7820016: Access M/J Comprehensive Science 2 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond)
2002055: M/J Comprehensive Science 1 Accelerated Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.7.SP.2.AP.4a: Identify the range (difference), median (middle), mean (average), or mode (most frequent) of two sets of data.
MAFS.7.SP.2.AP.4b: Make or select an appropriate statement based upon two unequal data sets using measure of central tendency and shape of the distribution.

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 1 - Seventh Grade Math State Interim Assessment:

This is a State Interim Assessment for seventh grade.

Type: Assessment

Formative Assessments

Cranberry Counting:

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

Type: Formative Assessment

Word Length:

Students are asked to use the mean and the mean absolute deviation (MAD) to compare two distributions.

Type: Formative Assessment

Overlapping Trees:

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

Type: Formative Assessment

Lesson Plans

Data Sets Represented in Computers:

This lesson shows how data can be represented by computers, in relation to everyday activities we may not be aware that we use computer. It gives an overview of graphing data by creating a histogram based on population data. Using the data collected, students will get a chance to hand write code to show what structure is needed for computers to collect, analyze and distribute such data. This lesson is lesson 1 of the Data Set and Deviation Statistics Unit and bridges statistical concepts of data collection, graphing and analysis with programming a computer using coding language while reinforcing foundational algebraic skills.

Type: Lesson Plan

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

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

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

Brr! How Cold is the Antarctic? :

In this PBL activity, students use online data to determine the extent of temperature changes in the Antarctic. They will analyze their data using measures of central tendency as well as measuring its variability. They will also use scratch to assist them in the calculations. These lesson will take two 50-minute periods.

Type: Lesson Plan

Perspectives Video: Professional/Enthusiasts

Field Sampling with the Point-centered Quarter Method:

In this video, Jim Cox describes a sampling method for estimating the density of dead trees in a forest ecosystem.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Nestle Waters & Statistical Analysis:

Hydrogeologist from Nestle Waters discusses the importance of statistical tests in monitoring sustainability and in maintaining consistent water quality in bottled water.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Camera versus Trap Sampling: Improving how NOAA Samples Fish :

Underwater sampling with cameras has made fishery management more accurate for NOAA scientists.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Statistical Analysis of a Randomized Study:

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.

Download the CPALMS Perspectives video student note taking guide.

Type: Perspectives Video: Professional/Enthusiast

Problem-Solving Tasks

How Long is 30 Seconds?:

The purpose of this task is for students to gain a better understanding of the passage of time. Students with the help of their teacher should work to design an investigation to find out how successful the class is at predicting when 30 seconds has passed. Once the data is recorded students should begin to graph their findings to make comparisons.

Type: Problem-Solving Task

Don’t Spill the Beans!:

The purpose of this task is for students to make a hypothesis, and then doing an experiment to test each students hypothesis. Students will collect and record their data, use graphical methods to describe their data, and finally analyze and interpret their results in the context of the activity.

Type: Problem-Solving Task

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 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

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.

Word Length:

Students are asked to use the mean and the mean absolute deviation (MAD) to compare two distributions.

Student Resources

Vetted resources students can use to 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

Virtual Manipulatives

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