# MAFS.6.SP.1.3

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.
General Information
Subject Area: Mathematics
Domain-Subdomain: Statistics & Probability
Cluster: Level 1: Recall
Cluster: Develop understanding of statistical variability. (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 of Last Rating: 02/14
Status: State Board Approved
Assessed: Yes
Test Item Specifications

• Assessment Limits :
Data sets in items must be numerical data sets.
• Calculator :

No

• Context :

Allowable

Sample Test Items (3)
• Test Item #: Sample Item 1
• Question: Tim drives the Grand Avenue bus route. The total number of people who ride the bus each week for 5 weeks is shown in the data table.

How many more people need to ride the bus in week 6 to increase the mean number of riders per week by 10?

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

• Test Item #: Sample Item 2
• Question: Linda recorded the number of minutes she practiced playing her violin for 10 days. The table shown represents the data she collected.

A. According to the data, what is the average amount of time Linda spent practicing per day?

B. What is Linda’s variation among all 10 days?

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

• Test Item #: Sample Item 3
• Question: Tim drives the Grand Avenue bus route. He records the total number of passengers each week for 4 weeks. The mean and mean absolute deviation of the data are shown.
• Mean: 17,123
• Mean absolute deviation: 611
Select all the possible numbers of riders for week 5 that are within the mean absolute deviation.

• Difficulty: N/A
• Type: MS: Multiselect

## Related Courses

This benchmark is part of these courses.
1205010: M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1205020: M/J Accelerated Mathematics Grade 6 (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 (current), 2022 and beyond)
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
2105030: M/J Advanced World Cultures (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 - 2023, 2023 and beyond)
2106015: M/J Civics (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 - 2023, 2023 and beyond)
2106016: M/J Civics & Career Planning (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022 (current), 2022 - 2023, 2023 and beyond)
2106020: M/J Civics, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022 (current), 2022 - 2023, 2023 and beyond)
2106025: M/J Civics, Advanced (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 - 2023, 2023 and beyond)
2106026: M/J Civics, Advanced & Career Planning (Specifically in versions: 2014 - 2015, 2015 - 2019, 2019 - 2022 (current), 2022 - 2023, 2023 and beyond)
2106030: M/J Law Studies (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 - 2023, 2023 and beyond)
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022 (current), 2022 and beyond)
2106029: M/J Civics and Digital Technologies (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 - 2023, 2023 and beyond)
2003030: M/J STEM Physical Science (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)
2002200: M/J STEM Environmental Science (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)
2001025: M/J STEM Astronomy and Space Science (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)
2000025: M/J STEM Life Science (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)
2109015: M/J World History and Career Planning (Specifically in versions: 2016 - 2019, 2019 - 2022 (current), 2022 - 2023, 2023 and beyond)
2109025: M/J World History, Advanced and Career Planning (Specifically in versions: 2016 - 2019, 2019 - 2022 (current), 2022 - 2023, 2023 and beyond)
7821024: Access M/J World History and Career Planning (Specifically in versions: 2019 and beyond (current))

## Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.6.SP.1.AP.3a: Solve for mean of a given data set using whole numbers.
MAFS.6.SP.1.AP.3b: Explain or identify what the mean represents in a set of data.

## Related Resources

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

## Assessments

Sample 4 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 3 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 2 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

Sample 1 - Sixth Grade Math State Interim Assessment:

This is a State Interim Assessment for sixth grade.

Type: Assessment

## Formative Assessments

Explain Measures of Variability:

Students are asked to list measures of variability and explain what they indicate about a set of data.

Type: Formative Assessment

Explain Measures of Center:

Students are asked to list measures of center and explain what they indicate about a set of data.

Type: Formative Assessment

Compare Measures of Center and Variability:

Students are asked to explain the difference between measures of center and measures of variability.

Type: Formative Assessment

## Lesson Plans

Analyze Data:

This lesson uses statistical analysis to evaluate data. The data used is from the app created by the students in lesson 2 of the Data Set and Statistics Unit. This lesson also guides students in recognizing the different types of data collected and how the distribution's shape can be affected when graphed at different intervals in histograms. This is the final lesson in the unit.

Type: Lesson Plan

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 mean and variation from the mean of sea ice loss.

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

Data Detectives:

In this lesson, students will become "Data Detectives" as they investigate that a measure for the center of 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. The students will utilize cooperative learning structures, hands-on learning activities and the Standards for Mathematical Practices as they delve into the world of understanding the concept of "mean" and numerical data sets.

Type: Lesson Plan

Universal GPA:

This lesson incorporates examples that are relevant to students' interests and uses diverse methods of presentation to demonstrate how changes in measures of variation can affect the measure of central tendency. The lesson utilizes the concept of grade point average (GPA) to create a real world example that student can relate to and apply. The lesson also includes a manipulative lab to demonstrate the idea of distribution of data as it relates to changing the value of a data point(s).

Type: Lesson Plan

Backpack Weight:

Just how heavy is your backpack? In this lesson students find measures of center in fun and meaningful ways. They will review mean, median, range and outlier, become a number set, and work together gathering and representing data about the weight of their backpacks.

Type: Lesson Plan

Calculating the Mean, Median, Mode, and Range from a Frequency Chart:

This lesson lasts a total of two hours: 15-minute pre-lesson, 90-minute lesson, and 15-minute follow up lesson or homework. Students will need the two worksheets, a mini-whiteboard, a pen, and an eraser. Each small group will need both card sets, a large sheet of paper, and a glue stick. Students will generate responses to a question about favorite computer games and use this data for the lesson. Students will then work collaboratively to display different data and discuss various strategy approaches.

Type: Lesson Plan

Flipping the house:

After reading the market report for the real estate sales in Miami during the first quarter, students will decide which type of property they want to consider for investment that can be sold during the next year and still make a profit from the sale. In addition, students will determine the best location to make the investment. Luxury homes are selling faster this year, while there is not inventory for single families houses. The median prices for condos and apartments are lower, but the number of sales is going up. Students also consider price fluctuation between different locations.

Type: Lesson Plan

Play Like you "MEAN" It! - Understanding a Measure of Center:

In this lesson, students will investigate how a measure of center, the mean, summarizes a numerical data set of all the values with a single number. Inquiry-based instruction along with hands-on learning is utilized to build understanding of the concept of "mean." Students will utilize Mathematical Practice Standards, as they build understanding of how the mean is used to describe a numerical data set.

Type: Lesson Plan

Data Doctors:

Have your students become "Data Doctors" by examining and analyzing means of central tendency. This lesson is a great introduction to mean, median, mode and range. Students will be sets of data, get to work in small groups examining the sets, learn a poem that will help them remember each term and take surveys to get real data sets.

Type: Lesson Plan

## Original Student Tutorials

Learn how to calculate and interpret the Mean Absolute Deviation (MAD) of data sets in this travel-themed, interactive statistics tutorial.

Type: Original Student Tutorial

It Can Be a Zoo of Data!:

Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.

Type: Original Student Tutorial

## Perspectives Video: Expert

Mathematically Modeling Hurricanes:

Entrepreneur and meteorologist Mark Powell discusses the need for statistics in his mathematical modeling program to help better understand hurricanes.

Type: Perspectives Video: Expert

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.

## Teaching Ideas

A Certain Uncertainty:

Students will measure the mass of one nickel 10 times on a digital scale precise to milligrams. The results will be statistically analyzed to find the error and uncertainty of the scale.

Type: Teaching Idea

Stem-and-Leaf Plots:

This lesson is designed to introduce students to stem-and-leaf plots as a graphical way to represent a data set. The lesson also reviews measures of central tendency with directions for finding mean, median, and mode are given. This lesson provides links to discussions and activities related to stem-and-leaf plots as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Teaching Idea

Drops on a Penny (Box-and-Whiskers Graph):

Students collect data, compute measures of central tendency, and create stem-and-leaf plots and box-and-whiskers plots.

Type: Teaching Idea

Measures of Central Tendency (Middle School):

"Students compute the measures of central tendency (mean, median, and mode) and range and determine how outliers affect the measures." from the Beacon Learning Center.

Type: Teaching Idea

All Numbers Are Not Created Equal:

Although a sheet of paper is much thinner than the divisions of a ruler, we can make indirect measurements of the paper's thickness.

Type: Teaching Idea

## Tutorial

Statistics Introduction: Mean, Median, and Mode:

The focus of this video is to help you understand the core concepts of arithmetic mean, median, and mode.

Type: Tutorial

## Virtual Manipulative

Box Plotter:

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

Type: Virtual Manipulative

## Worksheet

Splash of Math - SeaWorld Classroom Activity:

This resource allows students to assume the role of an ethologist provide 4 activities that challenge students to apply mathematics to solve complex real-life problems:

• Activity A: Watch the Whales - Determine average speed, distance, and percentage of time at the surface of gray whales.
• Activity B: Time Tally - From observations of a dolphin determine total time and percentage of time of certain behaviors.
• Activity C: Deep Divers - Determine average dive depth, diving time, and surface time of an elephant seal.
• Activity D: Breaches of the Humpback - Graph data and make a prediction from the graph. In this activity, the students will practice problem solving skills to solve complex real-life problems.

Type: Worksheet

## STEM Lessons - Model Eliciting Activity

Flipping the house:

After reading the market report for the real estate sales in Miami during the first quarter, students will decide which type of property they want to consider for investment that can be sold during the next year and still make a profit from the sale. In addition, students will determine the best location to make the investment. Luxury homes are selling faster this year, while there is not inventory for single families houses. The median prices for condos and apartments are lower, but the number of sales is going up. Students also consider price fluctuation between different locations.

## MFAS Formative Assessments

Compare Measures of Center and Variability:

Students are asked to explain the difference between measures of center and measures of variability.

Explain Measures of Center:

Students are asked to list measures of center and explain what they indicate about a set of data.

Explain Measures of Variability:

Students are asked to list measures of variability and explain what they indicate about a set of data.

## Original Student Tutorials Mathematics - Grades 6-8

Learn how to calculate and interpret the Mean Absolute Deviation (MAD) of data sets in this travel-themed, interactive statistics tutorial.

## Original Student Tutorials Mathematics - Grades 9-12

It Can Be a Zoo of Data!:

Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.

## Student Resources

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

## Original Student Tutorials

Learn how to calculate and interpret the Mean Absolute Deviation (MAD) of data sets in this travel-themed, interactive statistics tutorial.

Type: Original Student Tutorial

It Can Be a Zoo of Data!:

Discover how to calculate and interpret the mean, median, mode and range of data sets from the zoo in this interactive tutorial.

Type: Original Student Tutorial

## Tutorial

Statistics Introduction: Mean, Median, and Mode:

The focus of this video is to help you understand the core concepts of arithmetic mean, median, and mode.

Type: Tutorial

## Virtual Manipulative

Box Plotter:

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

Type: Virtual Manipulative

## Parent Resources

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