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.

This website from the BBC is a great introduction to averages (mean, median, and mode) and will take you through some interactive learning activities. A practice test and worksheet are also provided.

A tutorial to understand the three central tendencies and how to find them, as well as the standard deviation of values. Offers a discussion and practice problems.

Finding measures of central tendency will be applied to the different graphs throughout this unit.

Srudents connect mean, median, mode and range to real life. It will allow students to make sense of problems by using previously taught strategies.

Understanding how to interpret data by its shape, spread, and center helps students to understand statistics.

This lesson plan introduces quartiles and box plots. It contains an activity and discussion. Supplemental activities about how students can represent data graphically are also included.

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.

At the end of this lesson, students will be able to recognize and apply the concepts of mean, median, and mode in real-life problems.

Students analyze contextual situations, focusing on single variable data and bivariate data, and are introduced to the concept of using data to make predictions and judgments about a situation.

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.

Students visit second- and fourth-grade classes to measure the heights of older students using large building blocks as a non-standard unit of measure. They also measure adults in the school community. Results are displayed in age-appropriate bar graphs (paper cut-outs of miniature building blocks glued on paper to form bar graphs) enabling a comparison of the heights of different age groups. The activities that comprise this activity help students develop the concepts and vocabulary to describe, in a non-ambiguous way, how heights change as children age. This introduction to graphing provides an important foundation for creating and interpreting graphs in future years.

Brush up on your math skills relating to mean, median, mode, and range then try some practice problems to test your understanding.

This activity compares children's age to height to teach linear regressions. The handout includes notes for students and teachers with a step-by-step lesson on how to do three types of linear regressions - Best Fit line, Median Line and Least Squares Line.

Gain a basic understanding of mean, median, and mode by watching this easy to understand video tutorial. Additional resources are available as part of a paid subscription service. [11:03]

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.