Standard #: MAFS.912.S-ID.1.2 (Archived Standard)


This document was generated on CPALMS - www.cpalms.org



Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.


Remarks


In grades 6 – 8, students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points.

General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Statistics & Probability: Interpreting Categorical & Quantitative Data
Cluster: Summarize, represent, and interpret data on a single count or measurement variable. (Algebra 1 - Additional Cluster) (Algebra 2 - 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 - Archived
Assessed: Yes

Test Item Specifications

    Also assesses:
    MAFS.912.S-ID.1.3

    Assessment Limits :
    Items may require the student to calculate mean, median, and
    interquartile range for the purpose of identifying similarities and
    differences.

    Items should not require the student to calculate the standard
    deviation.

    Items should not require the student to fit normal curves to data.

    Data distributions should be approximately normal.

    Data sets should be real-world and quantitative. 

    Calculator :

    Neutral

    Clarification :
    Students will identify similarities and differences in shape, center, and
    spread when given two or more data sets.

    Students will predict the effect that an outlier will have on the shape,
    center, and spread of a data set.

    Students will interpret similarities and differences in shape, center,
    and spread when given two or more data sets within the real-world
    context given.

    Stimulus Attributes :
    In items that require standard deviation, the value should be given in
    the stem.

    Items should use real-world data and be set in a real-world context.



     

    Response Attributes :
    Items may require the student to apply the basic modeling cycle.

    Items may require the student to choose an appropriate level of
    accuracy.

    Items may require the student to choose and interpret the scale in a
    graph.

    Items may require the student to choose and interpret units.

    Items should not require the student to determine whether a
    distribution is left- or right-skewed.



Sample Test Items (2)

Test Item # Question Difficulty Type
Sample Item 1

Florida has 67 counties, and Texas has 254 counties.

The mean population for the state of FLorida by county is 291,834 with a standard deviation of 467,012.03, and the median is 107,056.

The mean population for the state of Texas by county is 104,127 with a standard deviation of 374,012.2261, and the median is 18,293.

Some of the data for both states are shown.

A business moves its corporate location from Texas to Florida. As a result of the move, 8,193 people move from the largest Texas county to the smallest Florida county, in terms of population.

Select all the population statistics that wil be affected by this population change.

N/A MI: Matching Item
Sample Item 2

A librarian in a large city collects data about his summer reading program. He collects data for two years, 2011 and 2012, on how many books are read each week. His ordered data sets are shown.

The librarian writes a summary about his data, as shown.

Click on each blank and select the appropriate word or phrase to complete the librarian's summary.

N/A ETC: Editing Task Choice


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Name Description
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Texting During Lunch

Students are asked to select a measure of center to compare data displayed in frequency tables and to justify their choice.

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Name Description
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"What's My Grade" is a lesson that will focus on a sample student's grades to demonstrate how a final grade is calculated as well as explore possible future grades. Students will create the distributions of each grade category using histograms. They will also analyze grades using mean and standard deviation. Students will use statistics to determine data distribution while comparing the center and spread of two or more different data sets.

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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.

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.

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?"

Birthday Party Decisions

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

In terms of soccer: Nike or Adidas?

In this lesson, students calculate and interpret the standard deviation for two data sets. They will measure the air pressure for two types of soccer balls. This lesson can be used as a hands-on activity or completed without measuring using sample data.

Marshmallow Madness

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.

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.

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.

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.

Who is the world's best ball player?

Students will use box and whisker plots to determine who is the better basketball player, Lebron James or Michael Jordan.

Centers, Spreads, and Outliers

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

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.

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.

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).

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.

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.

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.

Sweet Statistics - A Candy Journey

Students will sort pieces of candy by color and then calculate statistical information such as mean, median, mode, interquartile range, and standard deviation. They will also create an Excel spreadsheet with the candy data to generate pie charts and column charts. Finally, they will compare experimental data to theoretical data and explain the differences between the two. This is intended to be an exercise for an Algebra 1 class. Students will need at least 2 class periods to sort their candy, make the statistical calculations, and create the charts in Excel.

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.

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.

Representing Data 1: Using Frequency Graphs This lesson unit is intended to help you assess how well students are able to use frequency graphs to identify a range of measures, make sense of this data in a real-world context, and understand that a large number of data points allow a frequency graph to be approximated by a continuous distribution.
Representing Data 2: Using Box Plots This lesson unit is intended to help you assess how well students are able to interpret data using frequency graphs and box plots. In particular, this unit aims to identify and help students who have difficulty figuring out the data points and spread of data from frequency graphs and box plots. It is advisable to use the first lesson in the unit, Representing Data 1: Frequency Graphs (32498), before this one.
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.

Original Student Tutorial

Name Description
Movies Part 1: What's the Spread?

Follow Jake as he displays real-world data by creating box plots showing the 5 number summary and compares the spread of the data from surveys of the ages of moviegoers in part 1 of this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Perspectives Video: Experts

Name Description
Birdsong Series: Statistical Analysis of Birdsong

Wei Wu discusses his statistical contributions to the Birdsong project which help to quantify the differences in the changes of the zebra finch's song.

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?

Download the CPALMS Perspectives video student note taking guide.

Statistics and Scientific Data

Hear this oceanography student float some ideas about how statistics are used in research.

Perspectives Video: Professional/Enthusiasts

Name Description
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.

Winning the Race with Data Logging and Statistics

Data logging has transformed competitive racing! These SCCA drivers discuss how they use computers to compare multiple sets of data after test runs.

Revolutionize Wing Design with Equations and Statistics

Brandon Reese, a PhD candidate in the FAMU-FSU College of Engineering, discusses the significance of both Bernoulli's equation and statistical analysis for the design of a "smart wing."

Problem-Solving Tasks

Name Description
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.

Teaching Ideas

Name Description
Pump Up the Volume

This activity challenges students to analyze the statistical distribution of volume measurements from a partially filled graduated cylinder. The free app, GeoGebra is used to create a box plot to aid in the analysis.

An Ecological Field Study with Statistical Analysis of Two Populations

Students will design an investigation that compares a characteristic of two populations of the same species. Students will collect data in the field and analyze the data using descriptive statistics.

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.

Unit/Lesson Sequence

Name Description
Sample Algebra 1 Curriculum Plan Using CMAP

This sample Algebra 1 CMAP is a fully customizable resource and curriculum-planning tool that provides a framework for the Algebra 1 Course. The units and standards are customizable and the CMAP allows instructors to add lessons, worksheets, and other resources as needed. This CMAP also includes rows that automatically filter and display Math Formative Assessments System tasks, E-Learning Original Student Tutorials and Perspectives Videos that are aligned to the standards, available on CPALMS.

Learn more about the sample Algebra 1 CMAP, its features and customizability by watching the following video:

Using this CMAP

To view an introduction on the CMAP tool, please .

To view the CMAP, click on the "Open Resource Page" button above; be sure you are logged in to your iCPALMS account.

To use this CMAP, click on the "Clone" button once the CMAP opens in the "Open Resource Page." Once the CMAP is cloned, you will be able to see it as a class inside your iCPALMS My Planner (CMAPs) app.

To access your My Planner App and the cloned CMAP, click on the iCPALMS tab in the top menu.

All CMAP tutorials can be found within the iCPALMS Planner App or at the following URL: http://www.cpalms.org/support/tutorials_and_informational_videos.aspx

Virtual Manipulative

Name Description
Multi Bar Graph

This activity allows the user to graph data sets in multiple bar graphs. The color, thickness, and scale of the graph are adjustable which may produce graphs that are misleading. Users may input their own data, or use or alter pre-made data sets. 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.

Student Resources

Original Student Tutorial

Name Description
Movies Part 1: What's the Spread?:

Follow Jake as he displays real-world data by creating box plots showing the 5 number summary and compares the spread of the data from surveys of the ages of moviegoers in part 1 of this interactive tutorial.

This is part 1 of 2-part series, click HERE to view part 2.

Perspectives Video: Expert

Name Description
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?

Download the CPALMS Perspectives video student note taking guide.

Problem-Solving Tasks

Name Description
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.

Virtual Manipulative

Name Description
Multi Bar Graph:

This activity allows the user to graph data sets in multiple bar graphs. The color, thickness, and scale of the graph are adjustable which may produce graphs that are misleading. Users may input their own data, or use or alter pre-made data sets. 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.



Parent Resources

Problem-Solving Tasks

Name Description
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.



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