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In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Subject:
Mathematics
Statistics and Probability
Material Type:
Module
Provider:
New York State Education Department
Provider Set:
EngageNY
08/01/2013
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This learning video continues the theme of an early BLOSSOMS lesson, Flaws of Averages, using new examples—including how all the children from Lake Wobegon can be above average, as well as the Friendship Paradox. As mentioned in the original module, averages are often worthwhile representations of a set of data by a single descriptive number. The objective of this module, once again, is to simply point out a few pitfalls that could arise if one is not attentive to details when calculating and interpreting averages. Most students at any level in high school can understand the concept of the flaws of averages presented here. The essential prerequisite knowledge for this video lesson is the ability to calculate an average from a set of numbers. Materials needed include: pen and paper for the students; a blackboard or equivalent; and coins (one per student) or something similar that students can repeatedly use to create a random event with equal chances of the two outcomes (e.g. flipping a fair coin). The coins or something similar are recommended for one of the classroom activities, which will demonstrate the idea of regression toward the mean. Another activity will have the students create groups to show how the average number of friends of friends is greater than or equal to the average number of friends in a group, which is known as The Friendship Paradox. The lesson is designed for a typical 50-minute class session.

Subject:
Mathematics
Material Type:
Lecture
Provider:
MIT
Provider Set:
MIT Blossoms
Author:
Dan Livengood, Rhonda Jordan
02/13/2015
Educational Use
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Students act as R&D entrepreneurs, learning ways to research variables affecting the market of their proposed (hypothetical) products. They learn how to obtain numeric data using a variety of Internet tools and resources, sort and analyze the data using Excel and other software, and discover patterns and relationships that influence and guide decisions related to launching their products. First, student pairs research and collect pertinent consumer data, importing the data into spreadsheets. Then they clean, organize, chart and analyze the data to inform their product production and marketing plans. They calculate related statistics and gain proficiency in obtaining and finding relationships between variables, which is important in the work of engineers as well as for general technical literacy and decision-making. They summarize their work by suggesting product launch strategies and reporting their findings and conclusions in class presentations. A finding data tips handout, project/presentation grading rubric and alternative self-guided activity worksheet are provided. This activity is ideal for a high school statistics class.

Subject:
Mathematics
Statistics and Probability
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
Activities
Author:
Tom Falcone
05/03/2017
Educational Use
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Students learn a simple technique for quantifying the amount of photosynthesis that occurs in a given period of time, using a common water plant (Elodea). They can use this technique to compare the amounts of photosynthesis that occur under conditions of low and high light levels. Before they begin the experiment, however, students must come up with a well-worded hypothesis to be tested. After running the experiment, students pool their data to get a large sample size, determine the measures of central tendency of the class data, and then graph and interpret the results.

Subject:
Applied Science
Engineering
Material Type:
Activity/Lab
Lesson Plan
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Mary R. Hebrank
09/26/2008
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CC BY-NC-ND
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An introduction and examples of how to use Descriptive Statistics. It is about how we present and decribe the data in our sample in the best possible way. This covers tabels, graphs, measures of location and measures of spread/variability.

Subject:
Applied Science
Health, Medicine and Nursing
Mathematics
Statistics and Probability
Material Type:
Lecture
Provider:
Umeå University
Provider Set:
Quantitative Research Methods
Author:
Marie Lindqvist
Associate professor in epidemiology and biostatistics
11/01/2014
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Why is it important that students be careful what is posted for everyone to see? Students will investigate and discuss these questions during this module that directly relate to their daily life. Students will work cooperatively in groups to design an infomercial to be presented to elementary students and/or parents and community members. Key Learning Targets: I can use technology to produce and publish my work, and link to sources.I can include multimedia projects or visual displays when they will be helpful in clarifying and emphasizing information.I can actively participate and contribute to a discussion with my teacher and my peers. I can present my findings to a group or audience in a clear and concise way.I can create a storyboard to prepare a public service announcement. I can compare contrast trends of technology. I can write an explanatory paragraph to examine a topic (present and future digital footprint).

Subject:
English Language Arts
Material Type:
Lesson Plan
Author:
Jody Bauer
02/08/2018
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In this problem-based learning module, students will investigate why is it important that students be careful what is posted for everyone to see. Students will investigate and discuss these questions during this module that directly relate to their daily life. Students will work cooperatively in groups to design an infomercial to be presented to elementary students and/or parents and community members. Key Learning Targets: I can use technology to produce and publish my work, and link to sources.I can include multimedia projects or visual displays when they will be helpful in clarifying and emphasizing information.I can actively participate and contribute to a discussion with my teacher and my peers. I can present my findings to a group or audience in a clear and concise way.I can create a storyboard to prepare a public service announcement. I can compare contrast trends of technology. I can write an explanatory paragraph to examine a topic (present and future digital footprint).

Subject:
English Language Arts
Material Type:
Lesson Plan
Author:
Blended Learning Teacher Practice Network
11/01/2017
Educational Use
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Students use U.S. Geological Survey (USGS) real-time, real-world seismic data from around the planet to identify where earthquakes occur and look for trends in earthquake activity. They explore where and why earthquakes occur, learning about faults and how they influence earthquakes. Looking at the interactive maps and the data, students use Microsoft® Excel® to conduct detailed analysis of the most-recent 25 earthquakes; they calculate mean, median, mode of the data set, as well as identify the minimum and maximum magnitudes. Students compare their predictions with the physical data, and look for trends to and patterns in the data. A worksheet serves as a student guide for the activity.

Subject:
Geology
Physical Science
Material Type:
Activity/Lab
Provider:
TeachEngineering
Provider Set:
TeachEngineering
Author:
Jessica Noffsinger
Jonathan Knudtsen
Karen Johnson
Mike Mooney
Minal Parekh
Scott Schankweiler
02/17/2017
Educational Use
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Students explore the concept of the mean as they examine and compare scores for various sports events.

Subject:
Mathematics
Material Type:
Lesson Plan
Provider:
PBS LearningMedia
Provider Set:
PBS Learning Media Common Core Collection
Author:
U.S. Department of Education
WNET
07/25/2008
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Video with worksheet lesson on calculating mean and median (TI-84), determining shape of distribution based on relative values of mean and median.

Subject:
Mathematics
Statistics and Probability
Material Type:
Activity/Lab
11/23/2019
Only Sharing Permitted
CC BY-ND
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Subject:
Mathematics
Material Type:
Lesson Plan
Author:
Rylee Rutten
09/05/2017
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CC BY-NC
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Subject:
Mathematics
Material Type:
Full Course
Provider:
Pearson
10/06/2016
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Distributions and Variability

Type of Unit: Project

Prior Knowledge

Students should be able to:

Represent and interpret data using a line plot.
Understand other visual representations of data.

Lesson Flow

Students begin the unit by discussing what constitutes a statistical question. In order to answer statistical questions, data must be gathered in a consistent and accurate manner and then analyzed using appropriate tools.

Students learn different tools for analyzing data, including:

Measures of center: mean (average), median, mode
Measures of spread: mean absolute deviation, lower and upper extremes, lower and upper quartile, interquartile range
Visual representations: line plot, box plot, histogram

These tools are compared and contrasted to better understand the benefits and limitations of each. Analyzing different data sets using these tools will develop an understanding for which ones are the most appropriate to interpret the given data.

To demonstrate their understanding of the concepts, students will work on a project for the duration of the unit. The project will involve identifying an appropriate statistical question, collecting data, analyzing data, and presenting the results. It will serve as the final assessment.

Subject:
Mathematics
Statistics and Probability
Material Type:
Unit of Study
Provider:
Pearson
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Groups begin presentations for their unit project. Students provide constructive feedback on others' presentations.Key ConceptsThe unit project serves as the final assessment. Students should demonstrate their understanding of unit concepts:Measures of center (mean, median, mode) and spread (MAD, range, interquartile range)The five-number summary and its relationship to box plotsRelationship between data sets and line plots, box plots, and histogramsAdvantages and disadvantages of portraying data in line plots, box plots, and histogramsGoals and Learning ObjectivesPresent projects and demonstrate an understanding of the unit concepts.Provide feedback for others' presentations.Review the concepts from the unit.

Subject:
Statistics and Probability
Material Type:
Lesson Plan
09/21/2015
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Remaining groups present their unit projects. Students discuss teacher and peer feedback.Key ConceptsThe unit project serves as the final assessment. Students should demonstrate their understanding of unit concepts:Measures of center (mean, median, mode) and spread (MAD, range, interquartile range)The five-number summary and its relationship to box plotsRelationship between data sets and line plots, box plots, and histogramsAdvantages and disadvantages of portraying data in line plots, box plots, and histogramsGoals and Learning ObjectivesPresent projects and demonstrate an understanding of the unit concepts.Provide feedback for others' presentations.Review the concepts from the unit.Review presentation feedback and reflect.

Subject:
Statistics and Probability
Material Type:
Lesson Plan
09/21/2015
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In this lesson, students draw a line plot of a set of data and then find the mean of the data. This lesson also informally introduces the concepts of the median, or middle value, and the mode, or most common value. These terms will be formally defined in Lesson 6.Using a sample set of data, students review construction of a line plot. The mean as fair share is introduced as well as the algorithm for mean. Using the sample set of data, students determine the mean and informally describe the set of data, looking at measures of center and the shape of the data. Students also determine the middle 50% of the data.Key ConceptsThe mean is a measure of center and is one of the ways to determine what is typical for a set of data.The mean is often called the average. It is found by adding all values together and then dividing by the number of values.A line plot is a visual representation of the data. It can be used to find the mean by adjusting the data points to one value, such that the sum of the data does not change.Goals and Learning ObjectivesReview construction of a line plot.Introduce the concept of the mean as a measure of center.Use the fair-share method and standard algorithm to find the mean.

Subject:
Statistics and Probability
Material Type:
Lesson Plan
09/21/2015
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Subject:
Statistics and Probability
Material Type:
Lesson Plan
09/21/2015
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GalleryCreate a Data SetStudents will create data sets with a specified mean, median, range, and number of data values.Bouncing Ball Experiment How high does the class think a typical ball bounces (compared to its drop height) on its first bounce? Students will conduct an experiment to find out.Adding New Data to a Data Set Given a data set, students will explore how the mean changes as they add data values.Bowling Scores Students will create bowling score data sets that meet certain criteria with regard to measures of center.Mean Number of Fillings Ten people sit in a dentist's waiting room. The mean number of fillings they have in their teeth is 4, yet none of them actually have 4 fillings. Students will explain how this situation is possible.Forestland Students will examine and interpret box plots that show the percentage of forestland in 20 European countries.What's My Data?Students will create a data set that fits a given histogram and then adjust the data set to fit additional criteria.What's My Data 2? Students will create a data set that fits a given box plot and then adjust the data set to fit additional criteria.Compare Graphs Students will make a box plot and a histogram that are based on a given line plot and then compare the three graphs to decide which one best represents the data.Random Numbers What would a data set of randomly generated numbers look like when represented on a histogram? Students will find out!No Telephone? The U.S. Census Bureau provides state-by-state data about the number of households that do not have telephones. Students will examine two box plots that show census data from 1960 and 1990 and compare and analyze the data.Who Is Taller?Who is taller—the boys in the class or the girls in the class? Students will find out by separating the class height data gathered earlier into data for boys and data for girls.

Subject:
Statistics and Probability
Material Type:
Lesson Plan
09/21/2015
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CC BY-NC
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In this lesson, students are given criteria about measures of center, and they must create line plots for data that meet the criteria. Students also explore the effect on the median and the mean when values are added to a data set.Students use a tool that shows a line plot where measures of center are shown. Students manipulate the graph and observe how the measures are affected. Students explore how well each measure describes the data and discover that the mean is affected more by extreme values than the mode or median. The mathematical definitions for measures of center and spread are formalized.Key ConceptsStudents use the Line Plot with Stats interactive to develop a greater understanding of the measures of center. Here are a few of the things students may discover:The mean and the median do not have to be data points.The mean is affected by extreme values, while the median is not.Adding values above the mean increases the mean. Adding values below the mean decreases the mean.You can add values above and below the mean without changing the mean, as long as those points are “balanced.”Adding values above the median may or may not increase the median. Adding values below the median may or may not decrease the median.Adding equal numbers of points above and below the median does not change the median.The measures of center can be related in any number of ways. For example, the mean can be greater than the median, the median can be greater than the mean, and the mode can be greater than or less than either of these measures.Note: In other courses, students will learn that a set of data may have more than one mode. That will not be the case in this lesson.Goals and Learning ObjectivesExplore how changing the data in a line plot affects the measures of center (mean, median).Understand that the mean is affected by outliers more than the median is.Create line plots that fit criteria for given measures of center.

Subject:
Statistics and Probability
Material Type:
Lesson Plan