Section 3 Analyzing Data with Fathom Section 3 Analyzing Data with Fathom Summary Teachers analyze automobile data using Fathom to describe center and spread using dot plots box plots histograms They will examine distributions of univariate data of a quantitative attribute as well as comparison of distributions when a qualitative attribute is added to separate distributions by categories They will consider pedagogical issues related to the use of various graphical representations measures of center and spread and dynamic statistical software Objectives Mathematical Teachers will be able to generate questions to explore given a data set examine the distribution of a univariate data set using dot plots box plots and histograms including comparing distributions describe the center and spread of a data set using resistant median and interquartile range and nonresistant mean and standard deviation measures develop a conceptual understanding of the usefulness of the standard deviation Technological Teachers will be able to use Fathom to create dot plots box plots and histograms of univariate data add a qualitative attribute to an existing graphical distribution of a quantitative attribute both as a key legend and as a category on the y axis plot statistical measures on graphs compute basic statistics in a summary table Pedagogical Teachers will consider the advantages and disadvantages of dynamic linking capabilities and different graphical representations in Fathom consider how different graphical representations and measures of center and spread can draw attention to similarities and differences when comparing data sets consider the benefits and drawbacks of tasks to assist students in reasoning about data Prerequisites Material discussed in Section 1 of this module Vocabulary univariate data bivariate data interquartile range deviations standard deviation resistant measures and nonresistant measures Technology Files 2006 Vehicles ftm Emergency Technology Files 2006 Vehicles Part 3 ftm Required Materials Fathom v 2 Learning to Teach Mathematics with Technology An Integrated Approach Page 1 DRAFT MATERIALS DO NOT DISTRIBUTE Modified 9 22 2006 Section 3 Analyzing Data with Fathom Section 3 Analyzing Data with Fathom Data about an observed phenomenon comes in many different forms often frequencies scores codes categories or measurements In addition these different forms of data can be represented in multiple ways While viewing data in a table may assist in examining individual cases graphs and descriptive statistical measures may help in analyzing and characterizing trends in the whole data set or the aggregate Software tools have made the re presentation of data in graphs and the calculation of statistical measures quick and easy Thus rather than spending valuable time in constructing graphical displays or computing measures software tools facilitate quick displays and computations that allow for more time to be spent on analyzing the data In Sections 1 and 2 we used the software TinkerPlots to assist in analysis of data In this Section 3 and 4 we will be using Fathom 2 0 Key Curriculum Press 2005 TinkerPlots and Fathom use a similar interface to allow users to conduct data analysis TinkerPlots was designed to encourage users to create graphical displays by implementing a series of actions while Fathom allows users to easily create a variety of standard graphical displays with fewer actions While TinkerPlots has the capability to display measures of center on a graph Fathom includes a whole suite of tools that can allow users to compute descriptive and inferential statistics Thus Fathom is a much more powerful statistical tool while TinkerPlots is a powerful tool for analyzing data in graphical form Like TinkerPlots Fathom was created to allow users to have dynamic control over data meaning that as you change things in a document everything linked to what you are changing will update while you drag This linking between tabular data graphical representations and statistical measures can be a powerful tool for exploring data in meaningful ways We will start this Section with exploring univariate data a single attribute in a data set and will use what we learn with univariate data to explore bivariate data two attributes in a data set Learning to Teach Mathematics with Technology An Integrated Approach Page 2 DRAFT MATERIALS DO NOT DISTRIBUTE Modified 9 22 2006 Section 3 Analyzing Data with Fathom Part 1 Asking Questions from Data Increases in gas prices over the past several years may be one contributing factor to many automobile manufacturers focus on improving vehicle miles per gallon mpg performance and development of alternative types of engines that use a combination of electricity and gasoline Many people in America have also revisited the type of vehicle they own especially families who have longer commutes to the workplace To help us become more informed about the variety of vehicles on the market today we have assembled a collection of 41 vehicles manufactured in 2006 Most of the vehicles 30 were rated as the top fuel economy leaders in the most popular vehicle classes This data is depicted in the table on the following page Although a typical cycle of data analysis starts with forming questions and then collecting data to answer the question textbooks and teachers often use pre collected data sets with their students to provide an immediate springboard for exploring a phenomenon and to begin analyzing data When students are presented with a given data set they need to learn how to examine the data and formulate specific questions that can be answered knowing the various quantitative and qualitative variables called attributes in Fathom available about each case FOCUS ON MATHEMATICS M Q1 Review the data in the table Generate at least four different questions that you could explore by analyzing this data set FOCUS ON PEDAGOGY P Q1 Describe two classroom situations one for which it would be beneficial to use a pre collected set of data and one for which students should be collecting data themselves Provide a rationale for the benefits in each situation Learning to Teach Mathematics with Technology An Integrated Approach Page 3 DRAFT MATERIALS DO NOT DISTRIBUTE Modified 9 22 2006 Section 3 Analyzing Data with Fathom 2006 Vehicle Data Mfr Chevrolet Chevrolet Ford Ford Ford Ford Ford Ford Gmc Gmc Gmc Gmc Honda Honda Honda Honda Honda Honda Hyundai Hyundai Hyundai Isuzu Jeep Lexus