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.

In this video segment from TV411, figure skaters compute their average daily practice time.

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.

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).

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).

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.

Students explore the concept of the mean as they examine and compare scores for various sports events.

In this activity, students will be describing their partners imaginary outfit with "French slang" and also shopping online for clothes. Students will learn more about slang and online shopping in French culture. Students will also learn about clothing choices.

In this activity, students will practice describing clothing in French, so that others can guess what the item of clothing they're describing.

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.

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.

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.

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.

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.

Objectives:

1. Students will know the definitions for mean, median, mode, and range.

2. Given a data set, students will be able to find the mean, median, mode, and range.

This interactive escape room will allow students to practice their skills in mean, median, mode and range. There is also a video over how to solve all of those as well as some notes. 

Students experience data collection, analysis and inquiry in this LEGO® MINDSTORMS® NXT -based activity. They measure the position of an oscillating platform using a ultrasonic sensor and perform statistical analysis to determine the mean, mode, median, percent difference and percent error for the collected data.

This lesson will be a fun way for students to be create and use the collected data to find the measures of central tendency.