One Numerical Variable

  • A piece of mathematical wordplay-based art displayed in the 2024 Bridges Exhibition of Mathematical Art, Craft, and Design (see https://gallery.bridgesmathart.org/exhibitions/bridges-2024-exhibition-o...). The lowest level of understanding the arithmetic mean (Pre-K-12 GAISE II, p. 18) is a “fair share value” -- each person’s portion if a resource were shared equally. This is also a “levelling value” corresponding to the height x of the A’s extended crossbar, and x is the mean of the 4 letters’ heights if they were .5x, .5x, 2x, x. A higher level of understanding the mean is as a “balance point,” where A’s apex is the fulcrum placed where unit weights at M and E balance two weights stacked at N: the mean of the 4 weights’ x-coordinates is the x-coordinate of the fulcrum.

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  • This poem, written in July 2024 by Lawrence M. Lesser of The University of Texas at El Paso, is in the form of a bimodal distribution, reflected in the poem’s real-world context.  Before showing the poem, a teacher could first ask students to reflect on what they would expect a histogram of ages of pedestrians killed (or severely injured) to have and why (chances are some of their suggested rationale will  be captured in the poem!).

    Afterwards, students wanting to examine or discuss real-world evidence of such a distribution may look for data on their own, or be shown section 1.1.3 of 

    Roe, M., Shin, H., Ukkusuri, S., Blatt, A., Majka, K. et al. (2010), “The New York City Pedestrian Safety Study and Action Plan Technical Supplement,” New York City Department of Transportation. http://www.nyc.gov/html/dot/downloads/pdf/nyc_ped_safety_study_action_plan_technical_supplement.pdf . 

    This visual poem may also inspire students to write their own short statistics poem using (and connecting to) a data set with a differently shaped distribution.

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  • This haiku collection by Lawrence Mark Lesser from The University of Texas at El Paso was written in 2020 and won second place in the 2021 A-mu-sing Competition.  Each haiku in the collection addresses some property or real-world application of expected value that can be explored in class: the math and psychology in the structuring of an internationally syndicated game show (Deal or No Deal), tree diagrams (that students can do a calculation to verify in a realistic popular context of college basketball, showing how the EV need not correspond to the most likely outcome), an engaging probability paradox (in the context of the most popular animal Americans own as pets), the interaction with utility when making consumer decisions, a concrete visual analogy for a distribution’s expected value (inspired by Figure 2 of Martin’s July 2003 JSE article), and the concept of an estimator’s bias, and the how EV and mean express the same idea but in different contexts (random variable versus a sample, population or probability distribution). 

     

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  • A cartoon that  can be used to introduce ideas of the bias (degree of being on target) and reliability (degree of deviation) of estimators. The cartoon was used in the February 2023 CAUSE cartoon caption contest and the winning caption was written by Laurie Baker at the College of the Atlantic.  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 cartoon that can be used to help start a class conversation about how good visualizations are important for understanding and communicating data analyses. The cartoon was used in the September 2021 CAUSE cartoon caption contest and the winning caption was written by Ciaran Evans from Wake Forest University. 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 cartoon that can be used to highlight various features of the times series plots shown such as the seasonal trends perhaps signaling the oncoming storm in the cartoon. The cartoon was used in the July 2021 CAUSE cartoon caption contest and the winning caption was written by Larry Lesser from 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 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 cartoon that provides a clever way to introduce the statistical field of sabermetrics.  The cartoon was used in the May 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 about the trimmed mean as a robust measure of distributional center.  The lyric was written by Dennis Pearl from Penn State University in May 2023 and may be sung to the tune of the KitKat jingle - music by Michael A. Levin and lyric by Ken Shuldman used in the KitKat candy bar advertisements since 1986.

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  • A humorous cartoon to initiate a conversation about time series plots. The cartoon was drawn by American cartoonist Jon Carter in 2017.

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