# Data Presentation

• ### Art: The Levels of MEANing

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.

• ### Poem: Pedestrian Deaths by Age

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.

• ### Poem: Expected Value Haikus

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).

• ### Video: Lifetime Achievement Trophy

A video from the 2019 US Conference On Teaching Statistics where Dennis Pearl from Penn State University is introducing the winner of that year's CAUSE/USCOTSLifetime Achievement Award in Statistics Education.  He tells a story that can be useful in teaching the lesson that linear regression is inappropriate for making predictions well outside the range of the data. The story is loosely based on the phone call he made in ordering the trophy for the award.

• ### Cartoon: Refrigerator Art

A cartoon that  can be used in discussing how data visualizations help in thinking about the interpretation of data and stimulate critical thinking about the topic of the plot.  The cartoon was used in the March 2023 CAUSE cartoon caption contest and the winning caption was written by Larry Lesser at 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.

• ### Cartoon: Clowns and Targets

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.

• ### Cartoon: Red Carpet

A cartoon that  can be used to discuss the value of visualizations for displaying time series data. The cartoon was used in the December 2022 CAUSE cartoon caption contest and the winning caption was written by Dashiell Young-Saver, from IDEA Public Schools. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.

• ### Cartoon: Witches Brew

A cartoon that can be used in a discussion about ethical guidelines in reporting data and the importance of avoiding manipulations that represent what we hope to show while hiding opposing results also seen in the data.  The cartoon was used in the November 2022 CAUSE cartoon caption contest and the winning caption was written by Kim Bennett, from Georgia State 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.

• ### Cartoon: Recycling

A cartoon that can be a vehicle to discuss how finding an appropriate data visualization may require multiple revisions to ensure it is aligned with what is important in the data. The cartoon was used in the August 2022 CAUSE cartoon caption contest and the winning caption was written by Elise Lahiere, a student at Montclair State 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.

• ### Cartoon: Preparing Reports

A cartoon that highlights how the right visualization can communicate complex patterns in data more easily than written descriptions. The cartoon was used in the June 2022 CAUSE cartoon caption contest and the winning caption was written by Rob Carver from Stonehill College. The cartoon was drawn by British cartoonist John Landers (www.landers.co.uk) based on an idea by Dennis Pearl from Penn State University.