Is the iPod shuffle feature truly random? A simulation activity.

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Is the iPod shuffle feature truly random? A
simulation activity.

• Leigh Slauson
• Otterbein College
• Westerville, OH

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• The idea of randomness is fuzzy to most students
  and very often misunderstood to most students
  randomness is equivalent to an even distribution.
• In teaching sampling techniques, we often state
  that a simple random sample is the best way to
  draw a sample without drawing much attention to
  what makes a sample random.

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Other activities that address the concept of
randomness

• Random Behavior Section in Activity Based
  Statistics by Scheaffer, Gnanadesikan, Watkins,
  and Witmer

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• GAISE recommendations (ASA)
• Use real data
• Using real data sets of interest to students is
  also a good way to engage them in thinking about
  the data and relevant statistical concepts. There
  are many types of real data including archival
  data, classroom-generated data, and simulated
  data.
• Foster active learning in the classroom
• Active learning allows students to discover,
  construct, and understand important statistical
  ideas and to model statistical thinking.
  Activities have an added benefit in that they
  often engage students in learning and make the
  learning process fun.
• Use technology for developing conceptual
  understanding and analyzing data
• Perform simulations to illustrate abstract
  concepts

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• Background of this activity
• Article by Steven Levy in Newsweek in 2005
• From the day I loaded up my first Pod, it was as
  if the little devil liked to play favorites. It
  had a particular fondness for Steely Dan, whose
  songs always seemed to pop up two or three times
  in the first hour of play
• Case Study in Mind on Statistics, 3rd Edition,
  Utts and Heckard

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• Learning Goals iPod activity
• To helps students have a better understanding of
  the nature of randomness and to recognize what
  randomness looks like in reality.
• To demonstrate the value of simulations in
  modeling complex probability questions.

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• Classroom context
• Small liberal arts school
• Introductory Statistics Course
• College algebra prerequisite
• Class size about 30 students
• No computer access, but students are required to
  purchase a TI-83/84 calculator
• Variety of majors (math, nursing, athletic
  training, etc)
• Usually do this activity when the textbook gets
  to sampling plans, around week 7 of a 10 week
  quarter

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• Start the activity with a discussion of what does
  it mean to be random?
• Have they had the experience of hearing songs by
  the same artist either back to back or with in a
  short time frame?
• Share the Steven Levy article.
• Have students predict how likely it is to get
  repeated artists in a playlist of 15 randomly
  selected songs (out of nearly 1000 songs)

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Hand out a copy of my personal iPod Playlist
494 Bye Bye Bye N'Sync
495 Unforgettable Nat King Cole
496 Life Is Sweet Natalie Merchant
497 Kind And Generous Natalie Merchant
498 Jealousy Natalie Merchant
499 Pocketful of Sunshine Natasha Bedingfield
500 Unwritten Natasha Bedingfield
501 O.P.P. (Ultimix Remix) Naughty By Nature
502 Love Hurts Nazareth

• I created mine by simply copying all my songs out
  of iTunes and pasting them into an Excel file. I
  then assigned each song a number.

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Generating a random playlist
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• Random Number Table
• Have students (works best in teams of two)
  generate the random list of numbers by reading 3
  digits at a time from a provided table and match
  them to the numbered song in the playlist
• Show of hands of how many students had repeated
  artists.usually about 20 30 of students will
  raise their hands and 1 or 2 will have back to
  back songs
• Then show them with the results of 1000 randomly
  selected playlists of n 15 songs

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(No Transcript)
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Graphing Calculator

• Math -gt PRB -gtrandInt
• Drawbacks
• draws with replacement
• issues with new calculators set to the same
  starting random seed.

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• Computer simulations
• Done this with Minitab sample from columns
• Fathom instructions will be posted in a
  separate document on CAUSEweb.org
• Working on an applet

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Fathom
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After the activity
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• Some Related Assessment Questions
• from ARTIST database
• Explain the law of large numbers and why the law
  of large numbers keeps gambling casinos in
  business.
• from Activity Based Statistics
• A book review in the Los Angeles Times about
  discrimination against upper-class
  African-Americans contains the following example
  A Harvard law student says her professor tended
  to ignore the raised hands of the black students
  in class and then, suddenly, he would call on
  several black students in a row As if, she
  explains, the professor had suddenly realized
  that he was neglecting an important segment of
  the student body and had resolved to make
  amends. Discuss this quotation in light of what
  you have learned from this activity

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• References/Websites
• JSE Article about Activity Based Statistics
• http//www.amstat.org/publications/jse/v5n2/gnanad
  esikan.html
• Steven Levy Newsweek article
• http//www.newsweek.com/id/36583