Measures of Spread

  • A poem reflecting on the idea of standardization in statistics by Dane C Joseph from George Fox University in Oregon that earned an honorable mention in the 2025 A-mu-sing Contest. In his submission for the contest Dr. Joseph indicated:
    "I wrote this poem to highlight the essential importance of standardization to some of the most basic scientific and social endeavors. Far from a perfect solution to many of the sociopolitical, educational, and technological issues we face, standardization is still immensely powerful when aptly done and is arguably indispensable to our daily lives—from making policy and admissions decisions to calibrating instruments and building machines. My hope is that learners will acquire a sense of the tension between the usefulness and appropriateness of standardization, appreciate how very simple tools like Z-scores can help us to responsibly rank various objects, as well as openly critique why they can also lead to problems when the objects to be ranked and compared are human attributes. Among other things, instructors should encourage students to explore the meaning of the contrasting big 'M' little 'm' moniker, and allusions to central tendency (e.g., C grades)."

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  • A cartoon providing a nice way to introduce the Coefficient of Variation as a measure of relative variability in this era of virtual meetings. The cartoon was used in the September 2020 CAUSE cartoon caption contest and the winning caption was written by Larry Lesser from the The University of Texas at El Paso. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

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  • A song by Lawrence M Lesser written in 2022 to emphasize the idea that measures of variation like the standard deviation or IQR do not change with a shift in location.  May be sung to the tune of "Vacation", the 1982 hit by the all-female rock band, the Go-Go's.  The audio for this parody was produced by Nicolas Acedo Aguilar and the vocalist was Alexandria Campos, students in the commercial music program at The University of Texas at El Paso.

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  • A video using dance to teach about the concept of variance involved.  This 2013 video is from the “Dancing Statistics” series developed by Lucy Irving from Middlesex University (UK) funded by a BPS Public Engagement grant and additional funding from IdeasTap.  Full credits are within the video.   The Dancing Statistics project is described at https://www.frontiersin.org/articles/10.3389/fpsyg.2015.00050/full

    The video also comes with teaching notes for viewing by instructors who are logged into CAUSEweb.org. 

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  • These pages explain the following basic statistics concepts: mean, median, mode, variance, standard deviation and correlation coefficient (with example from the Institute on Climate and Planets).

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  • This website provides a comprehensive overview of descriptive statistics (mean/median/mode, range, standard deviation, and variance) through informative webpages with examples, links to data sets, and problems for the readers to try for themselves.

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  • A song for use in helping students to recognize how a change in units affects the variance (since variance is expressed in squared units).  Music & Lyrics by Tom Toce, ©2015 Retrograde Music.  This song is part of an NSF-funded library of interactive songs that involved students creating responses to prompts that are then included in the lyrics (see www.causeweb.org/smiles for the interactive version of the song, a short reading covering the topic, and an assessment item).

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  • A song to be used in discussing how the mean and standard deviation work well in describing symmetric distributions while the median and IQR are valuable when you need more resistant measures for skewed distributions. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of “Faithfully,” the 1983 ballad by the band Journey. Also, an accompanying video may be found at
    https://www.youtube.com/watch?v=b8lry78zBWE See also the companion song “Which Measure and Spread to Use” also written by Mary McLellan with the same learning objective.

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  • A song to be used in discussing how the mean and standard deviation work well in describing symmetric distributions while the median and IQR are valuable when you need more resistant measures for skewed distributions. The lyrics were written by Mary McLellan from Aledo High School in Aledo, Texas as one of several dozen songs created for her AP statistics course. The song may be sung to the tune of the 1976 pop song “Dancing Queen,” by ABBA. Also, an accompanying video may be found at
    https://www.youtube.com/watch?v=b5-wg3OYUIE See also the companion song “Which Measure Should I Choose” also written by Mary McLellan with the same learning objective.

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  • A quote to aid in discussing the foundational idea in statistics of the importance of understanding the nature of uncertainty. The quote is by Israeli-American educator, computer scientist, and co-founder of the Coursera online platform Daphne Koller (1968 - ). The quote is found in the May 3, 2008 New York Times story on Dr. Koller.
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