Instructor’s Guide

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Page ID: 81435

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Analytical Sciences Digital Library

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This module introduces students to ways of thinking about and working with data using, as a case study, the analysis of 1.69-oz packages of plain M&Ms. The module is divided into six parts:

Part I. Ways to Describe Data

Part II. Ways to Visualize Data

Part III. Ways to Summarize Data

Part IV. Ways to Model Data

Part V. Ways to Draw Conclusions From Data

Part VI. Now It’s Your Turn!

Interspersed within the module’s narrative is a series of investigations, each of which asks students to stop and consider one or more important issues. Some of these investigations include data sets for students to analyze; for the data in the module’s figures, you may wish to have students use the interactive, on-line version available at http://dpuadweb.depauw.edu/harvey_web/Data_Analysis/index.html.

Many of the investigations draw on a data set that consists of 30 samples of 1.69-oz packages of plain M&Ms, the general structure of which is shown here

**Table 2. Source, Distribution, and Net Weight of Plain M&Ms in 1.69-oz Bags**
bag	store	blue	brown	green	orange	red	yellow	net weight (g)
27	CVS	5	17	6	4	8	19	50.802
28	Kroger	1	21	6	5	10	14	49.055
29	Target	4	12	6	5	13	14	46.577
30	Kroger	15	8	9	6	10	8	48.317

The counts for the different colors of M&Ms were collected by students at DePauw University in the fall 1996 semester as part of an in-class exercise; this was the only data collected at that time. To allow for a consideration of grouping in this case study, samples were assigned randomly to one of three hypothetical sources. Because the original data did not include a consideration of mass, the net weights included in the data set were generated specifically for this case study by simulating the random sampling of single plain M&Ms from a normally distributed population of weights. The values of μ and σ for this population were derived using the mean, \(\bar{x}\), and the standard deviation, s, for the published weights of 462 plain M&Ms available through the Puget Sound Data Hoard (http://stat.pugetsound.edu/hoard/Default.aspx). The appendix to this Instructor’s Guide includes the R code used to generate these net weights, as well as the R code used to generate the figures that accompany some of the suggested responses.

This case study is meant to serve as an introduction to data and to data analysis and, as with any introduction, it considers a small number of topics, principally those covered in Chapter 4 of Analytical Chemistry 2.0; additional resources that provide a deeper introduction to data and to data analysis are listed in Appendix 1 of the case study.

Suggested responses are presented in normal font; additional comments, suggestions, and supplementary materials are in italic font.