# MiddleSchoolPortal/Statistics: Handling all that Data

<keywords content="middle school mathematics statistics lessons mean median mode plots graphs data analysis representation" /> <metadescription content="A free, standards-based, online publication developed for teachers offering digital resources that support the teaching of core statistics concepts in the middle school mathematics classroom." />

## Statistics: Handling All That Data! - Introduction

Data overwhelms our modern lives. How to make sense of the numbers in newspaper stories, in campaign speeches, in scientific experiments? Statistics offers tools to help us organize and interpret data. Even at the middle school level, students can work with statistics in real-world situations, whether actual or simulated.

In this publication, we offer lesson ideas on Teaching the Basics, those core statistical concepts to be covered in the middle school curriculum, such as the mean and the median, box-and-whisker plots, and scatter plots. Tools for Displaying Data supports this teaching. This section contains applets for creating representations of data, meaningful “pictures” that capture the data visually.

Beyond the required curriculum topics, sections on Activities and Projects offer problems, provocative questions, and hands-on experiments that engage students in their own collection and analysis of data.

## Contents

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Under Background Information for Teachers are professional opportunities for review of statistical concepts as well as resources for classroom support. The final section considers statistics in the NCTM Standards.

## Background Information for Teachers

Here are professional resources that offer deeper insight into statistical concepts, set out teaching strategies, and provide support materials for your work in the classroom.

Learning Math: Data Analysis, Statistics, and Probability This online workshop for elementary and middle school teachers introduces several ways to organize, represent, and describe data. Participants in this free, college-level course consider practical problems of designing experiments, such as random sampling, and explore basic ideas of probability. In a final session, teachers break into grade bands to explore ways to apply these concepts in classrooms. Each of the ten sessions in the workshop contains video segments, problem-solving activities, a guide for the workshop leader, and interactive activities online. This is one of the professional course offerings from Annenberg Media Learner.org.

Gallery of Data Visualization: The Best and Worst of Statistical Graphics This site offers graphical images that represent data from a range of sources (historical events, spread of disease, distribution of resources). The author contrasts the differences between the best and worst graphics by showing how some images communicate data clearly and truthfully, while others misrepresent, lie, or totally fail to "say something." If you are looking for innovative representations of data or examples of misrepresentation, you will find this resource helpful.

Dealing With Data in the Elementary School This project-based unit on statistics furnishes a vehicle for problem solving through real-world data collection and analysis. Students use the mean, mode and median to analyze their data and use graphs to represent their findings. As a professional resource, the unit provides an explanation of The Elementary Mathematics Research Model. Rather than being taught as isolated topics, the statistical tools are used in applying the research model to real situations. Teachers are guided in taking their students through the seven steps in the model.

## Teaching the Basics

These materials support the teaching of core statistical concepts at the middle school level. Some are strictly paper-and-pencil activities, while others depend on computer applets. But, even the applets offer ideas that you could adapt to classrooms without computers.

Statistics and probability. Grades 6-8 This MathPARTNERS unit contains seven lessons with hands-on learning activities for exploring statistics and probability with students in grades 6-8. Each lesson, with reproducible student materials, features an overview of the mathematics, preparation guidelines, teaching tips, and suggestions for how to use each activity to develop specific mathematics concepts. Statistics activities focus on posing questions, gathering data, identifying bias, understanding measures of central tendency, representing data with graphs, and interpreting data.

Numbers : Handling data These tutorials for elementary and middle school students provide the basic facts in three areas: graphs and charts, understanding averages, and probability. Each area includes fact sheets that explain key concepts in simple terms, plus practice sheets and quizzes.

RobertNiles.com: Statistics Every Writer Should Know Robert Niles, a journalist and producer for the LA Times, created this site to help other writers learn the basics of statistics. He explains many key concepts that are essential to report accurate, meaningful numbers and facts. After starting with the fundamentals of mean, median, and percent, Niles goes on to describe more advanced topics like normal distribution, margin of error, and data analysis. For each section, examples demonstrate proper usage of the techniques. A discussion of some frequently asked questions is also given, such as sample sizes and choosing the right statistical test for different kinds of data. MSP full record

Plop It! Users click to build dot plots of data and view how the mean, median, and mode change as numbers are added to the plot. MSP full record

Mean and Median This applet allows students to input up to 15 data values and investigate the mean, median, and box-and-whisker plot for the set of data they create. Questions are suggested in the Exploration section.

Exploring Data Using Histograms Build a data set and compare its histogram to its line plot. Vary the size of the intervals and explore how the histogram changes in response.

Box and Whisker Plots Given a line plot and its corresponding box plot, students can add points to the line plot and note how the box plot changes. An effective aid to understanding box-and-whisker plots!

Line of Best Fit This activity allows the user to enter a set of data, plot the data on a coordinate grid, and see the equation for a line of best fit as determined by the computer. Students can remove selected data points and immediately see the effect on the line of best fit and its equation.

Exploring linear data In a more complex lesson connecting statistics and linear functions, students construct scatter plots, examine trends, and consider a line of best fit as they graph real-world data. They also investigate the concept of slope as they model linear data in a variety of settings that range from car repair costs to sports to medicine. Handouts for four activities, spread out over three class periods, are provided.

## Tools for Displaying Data

This section offers applets for creating several types of data display. They can be useful for class presentations as well as for offering “pictures” of those long lists of numbers collected as data. Students can engage more easily with the visual displays and make better sense of their data through these interactive exercises. The last two tools offered here help in collecting all that data: a stopwatch and a spinner.

Create a Graph Students will learn how to create area, bar, pie, and line graphs. They are provided with information about what each type of graph shows and what the graphs can be used for, along with an example of each type of graph. They can create the graphs using their own data.

Bar chart (grades 6-8) This virtual manipulative enables students to make a bar chart, three to twelve columns wide and five to twenty rows tall. They can label columns and click on cells to make the chart. A special feature: Students can enter data as quantities, and then by clicking the percentage button, they can instantly see the percentage relationship of the quantities. MSP full record

Circle Graph This activity allows the user to graph data on a circle graph. Users can use predefined data sets or enter their own data. Especially good for showing examples of this type of display!

Histogram (grades 6-8) This virtual manipulative enables students to construct histograms to summarize data. They can, first, view examples of real-world data, such as the number of minutes between eruptions of Old Faithful, then clear the data and enter their own. Finally, students can switch the display mode and see the same data as a box plot.

Histogram This second applet for creating histograms offers as examples real-world data sets more appropriate for older middle school students. The applet automatically displays the number of elements in the data set, the mean and standard deviation, and a frequency chart along with the histogram for each data set.

Box plot (grades 6-8) This virtual manipulative enables students to construct box plots to summarize data. As students enter data into a table, the applet displays the minimum and maximum data values, the lower and upper quartiles, and the median. The number in the data set, the average, and the standard deviation are also shown.

Stem-and-Leaf Plotter This activity generates a stem-and-leaf plot from data that students enter. After examining the display, students are challenged to give the mean, median, and modes; feedback is immediate and answers given, if requested.

Scatterplot (grades 6-8) To visualize the relationship between two variables, a scatter plot is often used. Here students click on a point on a grid to enter data or add values to a list. The manipulative displays the data points but also a line of best fit and its equation, for those students studying algebra. Besides instructions on using the applet, you’ll find an interesting activity that engages students in comparing their height with their hand span.

Data picking In this interactive game, students create a table of data they collect from the onscreen characters and then select a scatter plot, a histogram, a line graph, or a pie chart that best represents the data. The amount of data increases and the type of data representation changes according to which of three levels of difficulty is selected. Tips for students are available as well as a full explanation of the key instructional ideas underlying the game.

Stopwatch Functions just like a real stopwatch as well as recording set times, accurate to the nearest tenth of a second.

Adjustable Spinner Users can create a game spinner with one to twelve sectors to look at experimental and theoretical probabilities.

## Activities

Looking for statistics that could engage middle school students? Here are problems, provoking questions, lessons, and even a game to stimulate work with data analysis in varied settings.

Bones : does drinking soda affect your health? In this activity, students read graphs and interpret raw data to determine if there is a correlation between drinking soda and the rate of bone fractures in teenage girls. Students are encouraged to organize data into tables to look for associations, but are cautioned that additional factors many influence the appearance of cause and effect.

Train race In this interactive game, students compute the mean, median, and range of the running times of various trains, then select the one train that will get to the destination on time. Players extend their basic understanding of these statistics as they try to find the most reliable train for the trip. Students can select one of three levels of difficulty. There are tips for students as well as a full explanation of the key instructional ideas underlying the game.

State Data Map Information can be represented in many ways, and this applet allows the user to represent data about the states using colors. The state with the highest data value is darkest; other states are shaded proportionally. Several sets of data are already entered and available for examination: state population, land area, representatives in Congress, gasoline usage, and more. Users can eliminate the data from any state in order to note the consequences, or enter their own data. A box plot accompanies each map representation, showing the data in a different but corresponding format.

Capture-recapture : how many fish in the pond? How is statistics used in the real world? This activity introduces the capture-recapture method as a statistical tool used by fish and wildlife experts to estimate the size of populations. Students are challenged to estimate the total number of fish in a pond, given the numbers of fish initially tagged and released, the tagged fish recaptured, and the total number of recaptured fish.

Using NBA Statistics for Box-and-Whisker Plots In this lesson, students use information from NBA statistics to make and compare box-and-whisker plots. After reviewing the concepts of minimum, maximum, median, upper quartile and lower quartile, students create three box-and-whisker plots for sets of data on the heights and weights of basketball players. In each case, the students consider the effects of changing one piece of the data, such as eliminating the height of the tallest player. Detailed instructions for the lesson, assessment options, and all materials are included.

Do women live longer than men? This activity opens with a graph that depicts the life expectancies of men and women born in the United States. Students are asked to estimate the greatest difference between genders in the years between 1920 and 1996. The Hint tells students how they should read the graph to determine the life expectancy for a woman born in 1920. Related questions encourage students to think about how the shape of the curve might be affected by changing the scale, as well as variables that affect trends in life expectancy.

Census : how many people live in the United States? This activity opens with a bar graph depicting low, middle, and high estimates of U.S. population growth between 2000 and 2100. Students are given two statements about population growth and asked to decide if the data support those statements. Related questions ask students to look for trends in additional data representations.

Working hours : how much time do teens spend on the job? To answer this question, students must interpret a bar graph to determine the average number of hours teenagers work per week. Related questions ask students to calculate averages for additional data sets. The Did You Know feature offers interesting statistics about the hourly wages and annual salaries of various occupations.

Soda : does it make a difference where you shop? This activity offers students a chance to compare soda prices from two stores using data displayed on a scatter plot. Students are shown how the line y = x can be used to analyze the data and draw a conclusion. The activity contains two different ways to find the solution, questions related to analyzing similar data from other fields, and family activities using data collected in the home.

Bias Sampling This activity offers students a chance to compare soda prices from two stores using data displayed on a scatter plot. Students are shown how the line y = x can be used to analyze the data and draw a conclusion. The activity contains two different ways to find the solution, questions related to analyzing similar data from other fields, and family activities using data collected in the home.

Accessing and Investigating Population Data: National Population Projections In this activity, students investigate population projections from 1990-2100 using data from the U.S. Census Bureau Web. Using the five specific population pyramids, students investigate population projection data for the United States over a 110-year period. They examine how the population data is distributed over time and explain what factors might contribute to these trends. An activity sheet and thoughtful questions, included in the lesson plan, guide the class investigation.

## Projects

To actually apply statistics to real questions, nothing answers like a class project. Students can get their hands on messy, raw data. Collecting and analyzing their data, displaying their findings and reaching conclusions — these may be your students’ best mathematical experiences of the school year!

Junkmail (a mini project) No one is immune from receiving junk mail, but just how much of it is really finding its way to your address? In this simple activity, data collection and analysis are a key part of a project to learn about the importance of recycling. For one week, students count and record the number of pieces of junk mail received in their homes. The display and organization of the data can be modified to address the data and statistics topics the class is working on.

RoadKill For this online project, students and teachers collect roadkill data in their community for analysis and compare their data to other areas participating in the project. The site provides a detailed protocol for monitoring and reporting roadkill, a method of reporting data through the web, and access to data collected by all participants. The project crosses many disciplines, including environmental science education and data analysis.

Numerical and Categorical Data In this unit of three lessons, students formulate questions that can be addressed with numerical and categorical data. They then collect, organize, and display relevant data to answer those questions. As they collect categorical data, they consider how to word questions and how to record and display the data. As they collect numerical data, they focus on how to obtain measurements and how to represent and analyze the data by describing its shape and other important features. The final lesson examines specifically the differences in representing and analyzing categorical and numerical data.

Boil, Boil, Toil and Trouble: The International Boiling Point Project Be part of an annual event: Enroll your class in this free Internet-based collaborative project. Students discover which factors--room temperature, elevation, volume of water, or heating device--have the greatest influence on boiling point. Students boil water, record their data, and send it via email to be included in the site's database of results. After gathering the data, activities focus on analyzing the compiled data to find answers to questions about how and why water boils.

The Global Sun Temperature Project Technology allows students from around the world to work together to determine how average daily temperatures and hours of sunlight change with distance from the equator. Students can participate in the project each spring, April-June. Students learn to collect, organize, and interpret data. You will find project information, lesson plans, and implementation assistance at the site.

Down the Drain: How Much Water Do You Use? This Internet-based collaborative project will allow students to share information about water usage with other students from around the country and the world. Based on data collected by their household members and their classmates, students will determine the average amount of water used by one person in a day. Students must develop a hypothesis, conduct an experiment, and present their results.

The Gulf Stream Voyage Here is an interdisciplinary project that uses actual data to help students investigate the science and history of the Gulf Stream. Math students can greatly benefit from the opportunity to collect data and draw conclusions based on the data. In the lesson called Current Now, students use real-time data and satellite images to determine how the Gulf Stream moves in the course of a year. In another activity, students use data about water temperature obtained from ships and buoys to determine the course of the Gulf Stream.

## SMARTR: Virtual Learning Experiences for Students

Visit our student site SMARTR to find related virtual learning experiences for your students! The SMARTR learning experiences were designed both for and by middle school aged students. Students from around the country participated in every stage of SMARTR’s development and each of the learning experiences includes multimedia content including videos, simulations, games and virtual activities. Visit the virtual learning experience on Statistics.

## NCTM Standards

In its overview to standards for the middle grades, the National Council of Teachers of Mathematics (NCTM) observes, “Middle-grades mathematics . . . needs to prepare students to deal with quantitative situations in their lives outside school.” Statistics enters the mathematics curriculum strongly here as a set of tools and concepts to make sense of the quantities of data encountered in the everyday world.

The expectation at the middle school level is that students will build on the statistical base acquired in earlier years. They will now formulate more complex questions, design studies, collect appropriate data, and represent their data graphically. New representations to be learned include scatterplots, box plots, and stem-and-leaf plots. To answer their questions and reach conclusions, students will then select and use statistical measures, including the mean and interquartile range, to analyze the data.

Teachers play a leading role in providing experiences that engage students in developing understanding of these statistical ideas. This publication aims to put in your hands standards-based teaching ideas that expand and support your own repertoire as you help your students deal with the quantitative world all around them.

For a full set of the expectations for the Data Analysis and Probability Standard, you can visit the online chapter at http://standards.nctm.org/document/chapter6/data.htm. Another valuable resource from NCTM is the book (with CD) Through Data Analysis in Grades 6-8.