MA.6.DP.1.2

Given a numerical data set within a real-world context, find and interpret mean, median, mode and range.

Examples

The data set {15,0,32,24,0,17,42,0,29,120,0,20}, collected based on minutes spent on homework, has a mode of 0.

Clarifications

Clarification 1: Numerical data is limited to positive rational numbers.
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 6
Strand: Data Analysis and Probability
Status: State Board Approved

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))
1205010: M/J Grade 6 Mathematics (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))
1204000: M/J Foundational Skills in Mathematics 6-8 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7812015: Access M/J Grade 6 Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MA.6.DP.1.AP.2a: Use tools to identify and calculate the mean, median, mode and range represented in a set of data with no more than five elements.
MA.6.DP.1.AP.2b: Identify and explain what the mean and mode represent in a set of data with no more than five elements.

Related Resources

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

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

Lesson Plan

The Penny Lab:

Students will design an investigation to collect and analyze data, determine results, write a justification and make a presentation using U.S. pennies.

Paired student teams will determine the mass of 50 U.S. pennies. Students will also collect other data from each penny such as minted year and observable appearance. Students will be expected to organize/represent their data into tables, histograms and other informational structures appropriate for reporting all data for each penny. Students will be expected to consider the data, determine trends, and research information in order to make a claim that explains trends in data from minted U.S. pennies.

Hopefully, student data reports will support the knowledge that the metallic composition of the penny has changed over the years. Different compositions can have significantly different masses. A sufficiently random selection of hundreds of pennies across the class should allow the students to discover trends in the data to suggest the years in which the composition changed.

Type: Lesson Plan

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

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

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

Jump or Be Lunch! SeaWorld Classroom Activity:

Students will predict how high they can jump and then compare the height of their jumps to how high a rockhopper penguin can jump out of the water. They will practice mathematical skills for determining averages.

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

Video/Audio/Animation

Soybean growth rate response to touch:

A time-lapse video showing differential growth rates for touch-treated seedlings and control seedlings. This would be appropriate for lessons about plant growth responses to environmental stress and graphing growth rate. Plants were grown in a vermiculite soilless medium with calcium-enhanced water. No other minerals or nutrients were used. Plants were grown in a dark room with specially-filtered green light. The plants did not grow by cellular reproduction but only by expansion of existing cells in the hypocotyl region below the 'hook'.
Video contains three plants in total. The first two plants to emerge from the vermiculite medium are the control (right) and treatment (left) plants. A third plant emerges in front of these two but is removed at the time of treatment and is not relevant except to help indicate when treatment was applied (watch for when it disappears). When that plant disappears, the slowed growth rate of the treatment plant is apparent.
Treatment included a gentle flexing of the hypocotyl region of the treatment seedling for approximately 5 seconds. A rubber glove was used at this time to avoid an contamination of the plant tissue.
Some video players allow users to 'scrub' the playback back and forth. This would help teachers or students isolate particular times (as indicated by the watch) and particular measurements (as indicated by the cm scale). A graph could be constructed by first creating a data table and then plotting the data points from the table. Multiple measurements from the video could be taken to create an accurate graph of the plants' growth rates (treatment vs control).
Instructions for graphing usage:
The scale in the video is in centimeters (one cm increments). Students could observe the initial time on the watch in the video and use that observation to represent time (t) = 0. For that value, a mark could be made to indicate the height of the seedlings. As they advance and pause the video repeatedly, the students would mark the time (+2.5 hours for example) and mark the related seedling heights. It is not necessary to advance the video at any regular interval but is necessary to mark the time and related heights as accurately as possible. Students may use different time values and would thus have different data sets but should find that their graphs are very similar. (Good opportunity to collect data from real research and create their own data sets) It is advised that the students collect multiple data points around the time where the seedling growth slows in response to touch to more accurately collect information around that growth rate slowing event. The resulting graph should have an initial growth rate slope, a flatter slope after stress treatment, and a return to approximately the same slope as seen pre-treatment. More data points should yield a more thorough view of this. This would be a good point to discuss. Students can use some of their data points to calculate approximate pre-treatment, immediate post-treatment, and late post-treatment slopes for both the control and treatment seedlings.
This video was created by the submitter and is original content.
Full screen playback should be an option for most video players. Video quality may appear degraded with a larger image but this may aid viewing the watch and scale for data collection.

Type: Video/Audio/Animation

MFAS Formative Assessments

Explain Measures of Center:

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

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 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

Parent Resources

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