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# 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.

### Clarifications

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
Domain-Subdomain: Statistics & Probability: Interpreting Categorical & Quantitative Data
Cluster: Level 2: Basic Application of Skills & Concepts
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 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

#### Formative Assessments

 Name Description How Many Jeans? Students are asked to select a measure of center to compare data displayed in dot plots and to justify their choice. Texting During Lunch Histograms Students are asked to select measures of center and spread to compare data displayed in histograms and to justify their choices. Texting During Lunch Students are asked to select a measure of center to compare data displayed in frequency tables and to justify their choice.

#### Lesson Study Resource Kit

 Name Description Measurement Matters This Lesson Study Resource Kit is an introductory unit on measurement for a Chemistry I course.

#### 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."

 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.

#### 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.

 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.