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.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.
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Also assesses:
- 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.
MAFS.912.S-ID.1.3
- Test Item #: Sample Item 1
- Question:
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.
- Difficulty: N/A
- Type: MI: Matching Item
- Test Item #: Sample Item 2
- Question:
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.
- Difficulty: N/A
- Type: ETC: Editing Task Choice
Related Courses
Related Access Points
Related Resources
Formative Assessments
Lesson Plans
Original Student Tutorial
Perspectives Video: Experts
Perspectives Video: Professional/Enthusiasts
Problem-Solving Tasks
Teaching Ideas
Unit/Lesson Sequence
Virtual Manipulative
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will use data to decide the ideal candidate for a college scholarship by computing the mean and the standard deviation. The student will present the data using the normal distribution and make recommendations based on the findings. Students will recognize that not all data can be presented in this format.
Model-Eliciting-Activities, MEAs, allow students to critically analyze data sets, compare information, and require students to explain their thinking and reasoning. While there is no one correct answer in an MEA, students should work to explain their thinking clearly and rationally. Therefore, teachers should ask probing questions and provide feedback to help students develop a coherent, data-as-evidence-based approach within this learning experience.
MFAS Formative Assessments
Students are asked to select a measure of center to compare data displayed in dot plots and to justify their choice.
Students are asked to select a measure of center to compare data displayed in frequency tables and to justify their choice.
Students are asked to select measures of center and spread to compare data displayed in histograms and to justify their choices.
Original Student Tutorials Mathematics - Grades 9-12
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.
Student Resources
Original Student Tutorial
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.
Type: Original Student Tutorial
Perspectives Video: Expert
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.
Type: Perspectives Video: Expert
Problem-Solving Tasks
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.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task
Virtual Manipulative
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.
Type: Virtual Manipulative
Parent Resources
Problem-Solving Tasks
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.
Type: Problem-Solving Task
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.
Type: Problem-Solving Task