Statistics and Measures of Dispersion

 

H. G. Wells wrote: "Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write." Faces of Mathematics, p. 168. (see bibliography) Last week was spent on collecting and organizing the data and applying the measures of central tendency to your data. This week will be spent on applying the measures of dispersion to your data and analyzing and drawing inferences from the data.

Assignment Project  Measures of Dispersion Normal Distribution

Readings Bello & Britton, Sections11.3-11.4 and Critical Thinking across the Curriculum Project: Charts and Graphs and Making Decisions (http://www.kcmetro.cc.mo.us/ longview/ctac/GRAPHS.HTM)

Web Resources These web resources have links to Measures of Dispersion and Interpreting Statistical Data.

Assignment

You are to finish up your project on statistics. This week will cover creating other types of charts, finding the Measures of Dispersion, using the Normal Distribution Curve, and finally putting it all together with an analysis including inferences from your data. Please read the Critical Thinking across the Curriculum Project: Charts and Graphs and Making Decisions (http://www.kcmetro.cc.mo.us/longview/ctac/GRAPHS.HTM) before you write your analysis. Remember to include all of these components with your project: 1) a collection of real-world data - you can: conduct a survey, take data off the Internet, collect data from a scientific experiment, or use any other real-world data you wish! 2) a histogram and some other chart which you find the "best" to reflect your data. 3) an analysis of your data which includes: a) the Measures of Central Tendency: the Mean, Median, and Mode b) the Measures of Dispersion: the Range and Standard Deviation c) the Normal Distribution Curve overlaying your histogram. (See Example.) To graph the Normal Distribution Curve overlaying your histogram, make sure that you have your histogram defined using the standard deviation for the range of values. Then, first plot the histogram polygon as an intermediate step to the normal curve. To understand the variety in the Normal Distribution curve, explore this shockwave distribution curve (http://ocelot.bio.brandeis.edu/pages/classes/InterpGenes/Project/stat4.htm) NOTE: You need to have the shockwave plug-in installed on your computer with your browser of choice! d) a paragraph analyzed your data and making some sort of "decision" around your data. For example, if you use volcanic data, you might be able to predict a possible pattern. NOTE: Before you reach a conclusion about your data, you ought to browse this classic article: Pitfalls of Data Analysis (or How to Avoid Lies and Damned Lies by Clay Helberg, M.S. http://www.execpc.com/~helberg/pitfalls/ You may use a spreadsheet, a graphing calculator, or applets on the Internet to work with your data!

Web Resources

Ask Dr. Math Site on Measures of Dispersion
http://mathforum.org/dr.math/problems/ivan.6.30.96.html

The Bell Curve - lesson plan with interactive activities on the normal distribution curve
http://www.shodor.org/interactivate/lessons/sm1a.html

BOX-AND-WHISKER PLOT Instructions
http://ellerbruch.nmu.edu/cs255/jnord/boxplot.html

Graphical Display of Quantiles: the Box-and-Whiskers Plot
http://franz.stat.wisc.edu/~rossini/courses/intro-biomed/text/Graphical_Display_of_Quantiles_the.html

Interactive Graph of the Normal Distribution - change the mean to 3 and try different standard deviations
to see what happens with the curve
http://huizen.dds.nl/~berrie/javastats.html

Introduction to Statistics for the Biomedical Sciences
http://franz.stat.wisc.edu/~rossini/courses/intro-biomed/text/text.html

with Graphical Display of Quantiles: the Box-and-Whiskers Plot
http://franz.stat.wisc.edu/~rossini/courses/intro-biomed/text/Graphical_Display_of_Quantiles_the.html

and

Stem-and-Leaf Plot
http://franz.stat.wisc.edu/~rossini/courses/intro-biomed/text/Stem_and_Leaf_Plot.html

Lesson Plan on Constructing Graphs for 5-12 grades -from The ExplorerTM, a collection of educational resources
(instructional software, lab activities, lesson plans, student created materials ...) for K-12 mathematics and science education.
Site has downloadable complete files!
http://explorer.scrtec.org/explorer/explorer-db/html/822981603-81ED7D4C.html

with the Lesson Plans on Statistics
http://explorer.scrtec.org/explorer/explorer-db/browse/dynamic/Mathematics/folder/b17.html

Sample Problems on Abuse of Statistical Data
http://www.shodor.org/interactivate/lessons/st3.html 

Slideshow on Measures of Dispersion - an overview of the concepts in slideshow format
http://www.plantbio.ohiou.edu/epb/instruct/quantmet/lectures/lec3/sld001.htm

with slide 10 on the Misuse of Statistics
http://www.plantbio.ohiou.edu/epb/instruct/quantmet/lectures/lec1/sld010.htm

Using box plots to compare - good graphic illustration for comparing data sets
http://www.stat.psu.edu/~resources/ClassNotes/ljs_06/sld019.htm

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